The Compass is definitely the best way to go if you are in the market for a compact SUV, that is IF you are actually going to use it for SUV-type things. If its just to ride the pavement to work and back in an urban environment then thats fine but you are just buying something for looks and to try to give off some specific persona. Nothing wrong with that it just means there is no reason to give more weight to things like the Jeep's superior 4x4 capability. If you ain't gonna use it (regularly, pretending like you plan to go camping and trail riding one time someday doesn't count) then don't weight it when making the decision. Pay more attention to the things that matter, like is your wife a super aggressive driver who has miniature battle royales on the freeway every single day? If and only if that is the case she might need to be concerned about the amount of power the current Compass offers. For anything below 65 MPH it does very well because of sufficient gearing to launch it and be effective at fighting traffic in the 35-50 MPH range. Its mainly freeway acceleration where physics exceed what the gearing can make up for. Its true the Limited trim is geared the highest and this does hurt accel a tiny bit but it also gives it the highest MPG potential, and I can say depending on your speed ours can hold an average of 30 MPG on a road trip if the conditions are right which is pretty great (more like 28 MPG when she is driving tho...)
Keep in mind, the alternatives she is considering are no faster. They are all sub-200 horse wagons, so give or take a few pounds and their gearing everything she is looking at is roughly the same amount of slow. You'd need to look at entirely different vehicles in a different price range from some "premium" brands to get any meaningful horsepower in a vehicle this size (see: Land Rover Discovery Sport). Need, of course, is subjective. I am screwed because my wife has a small turbocharged coupe she is now used to and she will never be happy driving a sub-200 horse vehicle ever again. We want her next vehicle to be at least all-wheel drive because we live in the sticks of Northern Minnesota, the only way to get power and all wheel drive is to open up the wallet wider I'm afraid. I put up with the lack of power in the Compass because I can always take her turbo for a spin to scratch that itch...
Anywho, I have never had any issues with the transmission shifting properly in our 2nd Gen Compass Limited 4x4. It works great. Really makes the most of the power available.
The infotainment in the Compass is great, better than Honda for sure. My mother has a 2016 CRV and it has "good" infotainment but Jeep/Chrysler hits some marks just a bit better, like actually having a GD volume knob, having physical buttons to mute the audio, turn off the screen (for nighttime driving), and also physical buttons for parts of the climate control that matter. They may have fixed some of this in the new models but the 2016 comes up short in this area. Otherwise their interiors are very comparable in terms of quality. I don't know about the Rogue, no hands-on experience there, but I came from a Nissan sedan into this Compass and I can say I will likely never buy another Nissan again. Their marketing is strong (or should I say, "the Marketing is Strong with this one" ?) but I'm not convinced Nissan delivers on what they purport to offer.
The only other thought I had was BE SURE TO GET EXACTLY WHAT YOU WANT THE FIRST TIME. You don't strike me as this kind of buyer but here on the forum we are up to our elbows with people who purchased a low-end Compass and then they want to "Upgrade" to the big Uconnect screen and stuff like that. Jeep has made it pretty difficult to do these kinds of things, if you think you want Sirius XM Guardian you better buy the Jeep with it from the get-go because you pretty much cannot add it after the fact.
In the sub-200 horsepower compact SUVs the Compass is a clear winner. I think it turned out that way by accident, because its the product of FCA wanting to build a reasonably priced AWD CUV and they basically said "We (Chrysler) are not in a position to make an entry into the compact SUV segment right now, lets put the JEEP name on this one and replace their dated CUV" and Jeep division replied "Hold the phone, you aren't going to put OUR name on this glorified car until it meets a minimum set of standards!" and then they battled internally until the Jeep side was satisfied that that the powertrain and suspension were good enough to be on a lot in the vicinity of the beloved Wrangler, and the Chrysler side was satisfied that the vehicle was of sufficient quality as to appeal to modern buyers while not being too expensive to produce. (Separately, they also battled the aesthetics out until it looked like it belonged on a lot with the Grand Cherokee. Search Google for the Fiat 500X if you want to know how bad this vehicle *could have* came out in the looks department).
Good luck with your decision making!