IMHO, anyone running anything less than a Mac Pro and is still on 10.6 should ask themselves why they would upgrade now if they have seen no reason to upgrade the past 2 opportunities. Besides the fact that every revision has left something important to someone at each level except for 10.6 that I am aware of since that was the most universal OS version which also kept the 2nd highest level of compatibly bloat next to 10.5. I still keep a 10.6 partition on my MacBook pros and only my 2010 MBP is eligible for 10.9 since thankfully apple did not allow all hardware (Intel compatible) upgrade or you would have seen disasters reported to the point of rioting.
John Galt (I can't get that movie character name out of my head, hehe.) was on the money in his explanation. While his analysis hits the nail nearly dead center on the nail, there are a few non-third party issues that can and does arise but you may not notice or care depending on how in tune with your system you may be or your level of expectation of what an OS upgrade will do for you rather than to you. (Slightly convoluted answer? Not really.)
Personally, I understand both sides of the discussion and have felt the disappointment in performance as I have run the upgrade on a few different models of varying age. I have deployed what I think David Stelly refers to a "facile" backup i.e. a full device clone to an external on all but one of my upgrades. The exception was the first iMac to be released with 10.8 with no optical drive.
Before I go any further I should mention I teach, use, maintain and manage Macs for a school district with 400 plus and counting from 10.4 to 10.9 revisions of eMac, iMac, MacBook pro 13,15, 17, and MacBook Air 11's in addition to a couple hundred iPads.
I think a lot of people made the upgrade who would have been more cautious if they charged even a few dollars. Something about free combined with some new eye candy and tricks added to the base OS rather than 3rd party facilitated a leap they were not ready for. Meaning, even I moved forward a little faster knowing what I already know and having experienced lesser growing pains in 10.8 than in 10.6-10.7 in terms of loss of 3rd party features or functionality. It is really important to keep in mind that if you rely heavily on things like express card support for legacy or simply the most diverse accessibility to multiple storage and peripheral devices, you should always hold of on moving to a new system until the bugs have been worked out and the drawbacks have been identified and then make sure you walk that tight rope with a net under you.
Regarding the upgrade to 10.9 on the latest hardware, it was surprisingly debilitating with regard to the extra OS demand on resources. Our machines came with 8 gigs of Ram with 2.66 Quad core i5's and they were pushing the envelope for the level of power I needed to run to my satisfaction. The average user doesn't see or feel it but they are not running as demanding a regiment nor are they monitoring other machines in the process. I did not experience horrific/catastrophic data loss (thankfully) with my external drives, but I did experience painful time sucking bugs that came simultaneously with Apple Remote Desktop bugs that brought unwelcome/unannounced changes in monitoring/viewing and workflow that clean installs on fresh machines still have not overcome the headaches that pre 3.7 versions did not incur. Having the knowledge that a few of my favorite utilities were and are still not as functional as they are on 10.8, I kept only the iMac on 10.9 because I was initially unable to restore it due to changes in port connectivity and the loss of the firewire port entirely which meant all sorts of adapter/thunderbolt workarounds and alternative methods of various types of recovery routes. Suffice to say that there is always a new wrinkle with new hardware and software upgrades speaking from a deployment perspective be it individual or mass.
I keep 10.6 on my quad and triple boot machines in order to run any legacy software and equipment that could lose access to hardware connections that 3rd party support has ceased. I lost connection via express card in previous upgrades but regained the connection with a reinstall of the software even when it was no longer updated but was simply removed by the install as incompatible yet a reinstall was successful with the original software driver support. This time I was not as lucky as I'm on borrowed time with the 17 discontinued and with it any developer's incentive to continue supporting older hardware like the eSata via express card. The new machines are great and we will all have to eventually move on and in doing so we get newer compatible and faster equipment. It is very disappointing to lose the use of perfectly good machines simple because updating the software renders prior functionality inoperable. Therein lies the pain of progress. It could be part of the "planned obsolescence" but in the case of Apple it is more likely the cost of remaining all things to all people is just not a viable business model.
I use multiple machines and the machines that shipped with 10.9 run fantastic. I connect to the same external equipment though different connections on different machines depending on that machine. You have to be prepared to leave some machines on an older system in order to maintain better performance and legacy compatibility and functionality as the case my necessitate. I have personal machines that are still running 10.7x due to older limitation by Apple and a 2010 MBP 2.66 i7 maxed at 8gigs of ram running memory clean with great success doing substantial multitasking with Adobe Photoshop, Aperture, and iMovie running all at the same time. It would run better with more RAM but that is no longer upgradeable. Doing this same combination on the 10.9 2.7 quad core i5 -1600MHz DDR3 and the 8gig option experiences some sluggishness and really feels like the OS and the expanded capabilities of new Apple Software updates has gone beyond what the machine can handle (due to the memory limitations that come from not maxing out at order time). Again, that is my power user activity on machines intended for the far less demanding needs of faculty and even students in the multimedia classes. Your mileage may vary.
Frankly, Apple downplays the risk to upgrading on older machines and does not go out of their way to warn of the potential ramifications. They seem to feel that if you run into trouble you should upgrade your hardware. Apple would have everyone on the 3-year renewal cycle. However, the trouble I see arising is the fact that new hardware not being upgradeable in RAM after purchase can substantially impact the ability to get through 3 years before software pushes the limitations of the hardware. This new pitfall IMO makes the need for maxing out the machine at purchase a hidden necessity for far more users than people suspect. Otherwise, a lot of users are going to become very dissatisfied with a non-upgradable after purchase option where they thought they could try to save a few dollars or chose that lesser expensive all in one.
Using a MacBook Air shipped with 10.9 and only 4 gigs of RAM is still very functional with the aid of the Memory Cleaner App. I feel that the 10.9 system is still leaking too much memory and the OS is too hungry for RAM. The new compression might work for some combinations of Apps but I've found ARD is not one those that work well without a lot more physical RAM. RAM cures a lot of ills but without after purchase options, that could be a serious hang-up beyond the lost hardware compatibility.
The features you pickup with each OS may not be necessary for you but carrot on the stick of things like iCloud key chain only working if you have 10.9 on at least one machine or the 10.7 mobile/me change to iCloud needed or the speech to text moving to 10.8 are the kind of little things (or not so little) that entice you followed by the discovery of the 2-10 things you just gave up to get them can be frustrating. (Aside from other failures that come from way to many 3rd party or individual user failures to maintain their machines)
Bottom line? You are on 10.6 this long for a reason. You may have waited to long and I can only imagine the combination of issues from leaping over 2 generations of upgrades. You are going to experience all of them without the benefits that came support during the incremental stages which could have been improved or completely dropped by now. So, backup and partition to find out. It is entirely likely that you may just be have to make new investments in equipment to take advantage of all that the new OS and software updates have to offer.
Personally, I like most everything in 10.8 better but again, they force upgrades to get specific features. This is the first time I've actually reverted personal machines to a previous version. Besides disabling a lot features I don't like in the newer versions of both 10.8 and 10.9, I don't like the performance hit that the machines suffer on 10.9 with only 8gigs of RAM when heavy multitasking with RAM demanding programs. Even with the help of Memory Clean, performance suffers on traditional mechanical hard drives. I can tell you that my MacBook Pro with 750gigs and 8 Gigs NAND RAM significantly smooths out the sluggishness that the iMacs without the NAND just can't overcome with more RAM.
Hope that was helpful.