FWIW:
I've been running Mavericks on my iMac since the general release. (I do Mac support for a living).
I have two Stardom-branded external drives attached, RAID 1, both of which have WD drives installed (either Green or Black). One is connected by FW800, the other by USB. One is my Time Machine backup, the other a data storage of 'stuff'. Both external drives are hardware-RAIDS, where the configuration is done inside the case, not via a software interface from outside.
In Disk Utility (set with Debug menu to show all partitions), they both now appear have an EFI additional 'partition' that appeared subsequent to Mavericks upgrade that wasn't there before. Both drives were attached when Mavericks upgrade was performed. Both drives are always attached and on. There have been several subsequent shutdowns and restarts of both iMac and external drives. To date, both drives have not had any issues, nor the iMac with the drives. All drive content is totally accessible. I've done nothing extra to faciliitate this since they were first attached with Lion then Mountain Lion.
I have also had various external FW800 drives (2.5"/3.5" in generic enclosures, Seagate and WD and Hitachi) attached to iMac 10.9, with files exchanged, unmount, on/off, remount without any issue. These drives, too, have an 'EFI" partition showing in DU, in addition to their own multiple partitions. These drives were formatted by Disk Utility as GPT with HFS+ journalled ages ago. No data loss issues. These drives have also been subsequently used with Macs of other system versions, with no issue.
Whilst I have had both WD and LaCie branded enclosures attached previously, I have *never* installed or used their management software - I have *always* re-partitioned and setup with Disk Utility.
I have also attached bog-standard and SanDisk USB 8/16GB thumb drives that have been formatted with DU. They too also show the new 'EFI' partition. There has not been any data lost from them either.
I also have a Synology NAS with SHR RAIDing on WD Red drives 'networkedly-attached' and no issues there either.
I have another 2 iMacs 10.9 with a 'generic' USB or FW800 enclosures over WD HDDs, as a TM backups and storage. Again, both partitioned and setup through DU (back at 10.7/10.8). Both were attached and on during 10.9 upgrades. Both still up and running as expected without an issue.
So to summarise, in my case, there are no hardware-specific issues with either branded or generic external cases, with either USB or FW or network attachment, RAIDed or not, regardless of HDD manufacturer, or whether attached during or after 10.9 upgrade or not. All external drives are either self-mananged or setup via Disk Utility - no third party software is involved.