In our white Trailhawk with the 9-speed, I would say that the shifting performance is comparable or faster than many similar cars. There is not an annoying lag in downshifting to pass for example. Mash on the accelerator and it downshifts faster than the resulting acceleration which is to say that the downshift is not what is slowing you down.
However, there is a noticeable delay when shifting from reverse to drive or vice versa. During the approximately 1 second for this shift it is in neutral - so with your foot off the brake while shifting R->D you will roll a non-trivial amount. Other transmissions I've driven do not have this R<-->D lag. It's enough to bump someone in a parking lot if you're lazy on the brake.
Thank you guys, so I hope I'll say goodbye to that issue if I finally can buy this Renegade! It was really annoying, and even dangerous sometimes, when you wanted to pass a car on road but you din't get instant response from the transmission.
The nine speed auto works terrifically. Responsiveness is good and shifts are quick. But note that it always starts in second gear unless you have it in auto-stick and purposely select first.
The car still gets out of the hole quite well in second gear. It won't shift into 9th gear until you exceed ~64 mph. So if you don't have 65 mph speed limits, you may never use 9th gear. It will hold onto 9th gear for a while if a very slight grade brings the speed down a little below 64. The engine doesn't have enough torque to climb any significant hill while in 9th.
I really like the 2.4 engine. I just wish it was available with the manual transmission (I wasn't impressed with the 1.4T manual that I drove).
We haven't noticed anything, specifically I have only driven it once, I'm a passenger most of the time. But I used to be a Jeep mechanic years back, I think the power and shifting with the Trailhawk are fine. Compared to a Patriot/Compass it's a powerhouse, Patriot felt like it had trouble leaving a stop sign.