The question isn't "which flavor of OS X will it run?" because it will run both.
The tablet will have both an x86 chip (an Atom, dual-core (N330) as an option) and an custom ARM SOC (system on a chip). You'll be able to hot-switch between a modified iPhone OS and touch-optimized 10.6. However, the hot switch may or may not involve booting the Atom system as once it boots, if you switch to the ARM chip, the Atom side will go into Sleep (10.6 has Sleep optimization, so it'll be nice and smooth).
The "iPhone" OS version for the tablet will be, of course, optimized for the tablet and able to run current iPhone software, and not just one at a time. However, if the users wishes to do more complex work and needs more processing power, they can boot up the Atom system. The SOC will continue to run as it requires very little power, and will communicate things like push messages to the Atom side, per user settings.
Once the Atom system is booted (and it will boot fast, SSD + 10.6), the transition will be very smooth between the two.
Proper iTunes sync will, of course, work, but it can, if the user so wishes, keep the Mail apps of both simultaneous, as well as some others. The Atom side will be able to update the SOC as well as restore it - no need for another computer. Critical software update on the road? No problem. Need to install 10.6.2? You can tell the tablet to not sleep the Atom side while you continue working on iPhone OS.
Apple has never liked using a separate partitions for data and applications (many PC users do this so they can completely wipe and reinstall their OS of choice (be it Linux, Windows or another) without losing all their documents and photos in the process).
The SOC will have its own memory, as very fast sync removes the need of accessing the other side's drives (and the issues that come along with that). Files will be duplicated between the two systems, though the user is in power to choose what the SOC side has.
Only the Atom system will have access to the tablet's ports (except, of course, the 3.5mm jack). The user will be able to pick which system is using the stereo speakers/audio jack - so music can continue to come from iPhone OS while the user switches back and forth accomplishing different tasks.
Due to tech constraints the two systems will have separate Wi-Fi antennae. Although this can be a very slight nuisance for the user, it means that they can save power by killing AirPort on the Atom side and only browsing on the SOC. It also means they can use two networks at the same time on the tablet. The Atom side's antenna will be more powerful.