Fellow Sufferers,
An update (though premature to cast it as a solution).
I begin with some facts/observations about my own case. I'm not sure which are relevant, but some combination (a subset of these) is likely shared by many of us. My operating assumption is that a specific, identifiable set of symptoms more likely points to the same underlying problem. Even though it is possible that we are all experiencing approximately the same effects tracing back to distinct causes, it seems bad science to presume a multiplicity of causes for the same general observables. That's a long winded way of expressing doubt that the slowness of TM backups in one case is due to a WD drive incompatibility and in another case it is due to unsupported NAS drives (that work with earlier OSs despite being just as "unsupported" then) and in yet another case is some sort of persistent Time Capsule issue. If we are all having slow TM backups post Mavericks, given different drives, different connectivity, different modes of os upgrade (clean, restored, updated, cloned, migrated, etc), then Mavericks seems to be the common denominator. Thus, I'm hoping to narrow down the aspects of the Mavericks upgrade relevant to the TM problem. Since I am now 45GB into a 125GB backup (over wifi to a time capsule with an existing sparsebundle and no resetting of the TC), I think I'm onto something. My machine reports an estimated 3 hours to finish the 75+ gigs. All looks promising.
Now the observations:
I did a "clean" install of Mavericks while booted from an external USB drive containing the Mavericks installer. I'd had my TM backup, since my regular backup protocol was unproblematic under 10.8. Two machines backup to the same 2TB TC. The other, a 2011 MBP, has enjoyed uninterrupted performance following an in-place upgrade from 10.8 to 10.9 (i.e., no reformatting or booting from a different drive).
In addition to my existing TM backup, I cloned my home folder and a few global settings using Carbon Copy Cloner. I also manually copied a few key items to cloud space (my documents, iphoto library, etc). I've lost data before: once burned, twice cautions.
After the fresh install, I booted into the new volume, repaired permissions, updated via the app store (including the installation of "new" apps, like iphoto and iwork). Repaired permissions again and booted into an external volume (the one from which I did the installation, running 10.8 and containing all of my utilities). I ran Diskwarrior, which reported no problems, and then copied over my pics, music, docs, and the like. Booted back into my mavericks volume and commenced to redownloading the software I need for daily life (dropbox, ram cleaner, temp gauge, and so on). Repaired permissions again and attempted to setup TM. That's when I discovered two critical problems. (1) crazy-slow backup performance; (2) iWork. Once I realized that the estimates of 5-6 days to complete a backup were stable, I halted the process. I verifying the sparsebundle (all seemed ok), and I repaired the permissions on the backup image, which also seemed okay. I then attempted a backup via the usb ethernet dongle. Same speeds. Halted the process and attempted to repair the sparsebundle with DiskWarrior. It reported insufficient RAM and recommended that I boot from the CD, which wasn't an option, since I can't mount networked volumes when booted from the CD. So, I spent the night copying the sparse bundle from the TC to an external drive. The data was only about 200-250GB (absurd that I just said "only" 200GB!) but the image registers the capacity of the TC drive. So once it was copied over to the external drive, I shrank the image to 250 and attempted to use DW again. Same memory error. This was on a 1TB drive, so there was ample working space. I then moved to my wife's MBP with 8GB of RAM; still that error. I abandoned that approach.
By this time I realizes that the new iWork is a sucking chest wound where once there had been a serviceable productivity suite. So, I restored my 10.8 environment from the TC, and all went reasonably well. Took better than 13 hours, but that's not terribly slow for a full TM restore, as I recall. Booted, repaired and retrieved my cloud-stored iWork documents, lest they be befouled by The Abomination (iWork for iOS, bundled as iWork for Mavericks). Tragically, in my unreflective enthusiasm I updated my ipad's version of iWork and worried that this would corrupt the many documents in the cloud, documents I wanted to continue using with my restored iWork '09. Anyway, I concluded that the problem was not with TC or with the sparsebundle, since restoring my machine went fine.
Once I'd salvaged all of my documents, I attempted to figure out why the new OS wasn't cooperating with the existing backup. Many of you (6+ pages of comments on this thread alone by then) reported problems with Spotlight and various differences in performance depending on connectivity (USB, FW, TB, E-net, etc). Some reported intermittent success following factory resets, reformatting, and so on. But no clear, stable solution.
I resolved to maintain a "backup" manually until the end of the semester (I'm a teacher and really should not have broken my private policy of not dicking around with my setup during the term; I am weak). But then I noticed that quick look didn't work. And the default apps were wrong, and wouldn't change. For example, "get info" on a pages document revealed that Preview was the default app for the file type and when I manually selected Pages and applied to all, it seemed to execute, but none of the other ".pages" documents reflected this change. Permissions repair and reboot had no effect. I also noticed that spotlight searches came up empty, even when I knew the file existed. (I'm lazy and almost never navigate to things when CMD-space will get me there.). Then I started getting errors on all of my cloud services (dropbox, box.com, and googledrive all reported permission errors). I'd still not connected all of this up, so I just had all of the content restored from the cloud, overwriting the stuff I restored from my pre-upgrade clone.
Then, iTunes denied access to google play music manager (I have an android phone), despite the fact that all of these services worked flawlessly on 10.8.
Finally, the Mavericks version of Onyx came out. (Love, love, LOVE this utility.). It reported a damaged file structure and instructed me to repair it via the recovery partition. I'd verified the 10.9 volume from within the same 10.9 volume and it checked out, and I'd run a check from both DiskWarrior and Disk Utility on a 10.8 volume (while booted from the 10.8 volume), and none of these attempts to test it revealed problems. But onyx caught it. And the 10.9 recovery partition seems to have repaired it. I then used onyx to purge everything it would allow, every cache, every cookie, every font. It detected several corrupted plist files--specifically having to do with iWork. I did NOT upgrade to the new iWork after restoring my machine, recall. Yet, the plist for iWork was v3.0 instead of '09 (with the Mavericks creation date, even). Tried deleting it, but the new one created following a reboot was the same, v3. Finally copied the plist from my clone, which changed the version number to 3, but kept the creation date the same as for iWork '09.
Two things to note. After onyx purged everything and rebuilt everything rebuildable, spotlight took almost four hours indexing the startup volume.
I initiated a TM backup almost 3 hours ago. I had 125GB to backup. It is 67GB into and the system estimates another 2 hours remaining. So 5 hours to do a 125GB backup over wifi. Not bad.
Another thing to note. All of my home folder permissions remain dorked--where the get info should show "Staff" as read/write, it has a ghosted "Fetching ..." and "custom." It would seem that the fairly permissive dragging and dropping form of "migration" is not all that successful under 10.9. The usual advanced features context menu in accounts seems fine--the user ID is 502 and the group is staff. I didn't want to monkey about while the backup is running so smoothly. But, when it is done, I'll probably boot into the recovery partition and reset ACL permissions (though Disk Utility is not spitting out ACL permission errors). I do recall encountering this particular problem years back and using terminal to repair it, but I'm hesitant to employ older terminal commands in a wholly new OS. **** even making hidden files and folders visible requires a slightly different command.
My new fledgling theory: the culprit is migration problems that generate permissions problems neither detected nor repaired by Disk Utility (or third party utilities, even the undeniably awesome DW) ... unless booted into the recovery partition using the 10.9 disk utility there. Onyx was the crucial diagnostic tool in my case. Probably still needs the ACL reset too. And, if I really wanted to play it save, I probably should have reinstalled iWork '09 from the DVD instead of restoring from the clone. Might have been nice had we been cautioned that one would need to actually migrate data to the new volume, not just copy it over. Assuming that's the problem.
Whew. You're a champ if you read this far. I think the fix (for me) involved repairing the 10.9 volume from the recovery partition and using onyx to force various rebuilds, spotlight in particular. I do not know why spotlight didn't index post update, or didn't do a thorough one when I dragged all of my files into my home folder. Historically, (a) lots of new data copied to the drive triggers a reindexing and (b) it's obvious when this happens (fans blow, machine gets sluggish, clicking on the spy glass shows indexing, ram dwindles, activity monitor shows a lot of mds action, etc). There was no massive indexing post installation.
Also of concern: I had installed Temperature Gauge, which I downloaded from the app store (and wicked miss). But console listed scads of smc errors pointing to either the temp app or the ram app. Uninstalling the temp app and doing an smc reset (and pram zap, just for the **** of it) seems to have coincided with the elimination of those errors. But it's too early to say they are gone for good. And I can't be sure that all of the other stuff didn't cure it.
Hope this ridiculous data-dump proves useful to others as you attempt to diagnose yourselves to TM nirvana. (About an hour left to my first post-10.9 backup.)