Yes, I believe it's the same transmission, the 42RLE or whatever the number is.
One immediate difference you'll find is that there is no way to check transmission fluid on the 08. (I can hear it now

). At the top of the transmission dip stick tube is a little rubber plug saying to contact the dealer for service.
I'm not sure if this is a good thing or a bad thing. Since it's a lifetime warranty, I guess it's not all bad.
It does shift way different than my 04 Liberty. I don't know how to explain it, but it shifts different.
One thing that always drove me crazy on my 04 was that it went into overdrive at about 40 MPH and was hard to get it to downshift out of OD. I'd really have to push the gas pedal to get it to downshift and even then, it seemed to hesitate or something. There is one onramp to the freeway that drove me bonkers everyday with the 04, when I was going home. I've seen others post about the exact same thing, so I assume anyone with a KJ knows what I'm talking about. I'm not sure if it was addressed on later model KJ's or not.
The KK shifts a LOT different than my KJ did. Where the KJ was a very smooth, almost mushy shift, the KK seems to be a harder more agressive shift. I'm not sure how to explain it. You'd just have to drive a KK to experience it I guess
If I'm doing some moderate acceleration in the KK, and listening to the engine, and watching the tachometer, I'd almost swear that the engine is shut off at the point of shift, then turned right back on. Again, I don't know how to explain it, but it's a more aggressive, positive shift over my KJ.