I used to have a Kinesis Advantage; switched to it from a stock ErgoDox and then switched from it to a more customized ErgoDox. The way I see it is following:
firmware: Kinesis Advantage 2 is super convenient; ErgoDox or Kinesis Advantage modded with a generic controller are very powerful; original Kinesis Advantage was awful in practice (firmware bugs, inconvenient remapping etc.)
form factor: Kinesis Advantage/Contoured is bulky... very bulky. ErgoDox, on the other hand, fits in a shoe case... unless you have some larger case or a tray/dock, which is kind of necessary for typing in ones lap (balancing each half on a thigh is annoying).
keys: Kinesis Advantage ships with limited switch/keycap options (the keycaps are only thin OEM-profile ABS too); so does ErgoDox EZ (albeit there are at least PBT caps), but with a bit of DIY you can whatever you like, basically. BTW the Kinesis keyboards have a buzzer that can activate on switch actuation; something similar can be added to ErgoDox with some effort.
ergonomics of main sections: Contoured key wells versus flat halves are two different approaches with their own pros and cons. The key wells (Kinesis Advantage) are more comfortable with stationary hands, while a flat keyboard works better with typing style based on moving whole arms (kind of like playing a piano). I guess it's more of a personal preference. Kinesis Advantage has a small plus in putting columns for different fingers into different heights, and so especially pinkies don't strain as much when moving around.
ergonomics of thumb clusters: ErgoDox thumb clusters are commonly criticized for their placement and I agree with that, but it can be mitigated by using the 80key layout (each 2u key split into two 1u keys) with aggressively sculpted keycaps in my experience. Kinesis Advantage feels a bit better, because the thumb keys are on a different plane than the other keys, but I would prefer an even more agressive shape (see, e.g., the ManuForm custom keyboard) and more keys (thus the 80key ErgoDox).
wrist ergonomics: Kinesis Advantage is an one-size-fits-all solution, which means it works fairly well for an average person. If you prefer more tenting or a different hand separation, though, a fully split keyboard like stock ErgoDox always wins... but it takes some messing around and perhaps even DIY. I had another complaint about Kinesis Advantage—it sort of forces one to use the palm rest and thus a certain wrist-forearm angle... I prefer a slight negative slope though, and so I had to raise the front edge of the keyboard, which was a bit tricky due to weirdly contoured surfaces all over the keyboard (another example is placing a trackpad into the empty space between key wells; it has to be taped not to wiggle).
