Went from an '06 Mustang to a '17 Mustang at the start of this year. It's my first push button start. I actually like it. The thing I like the most is the whole keyless part. Just keep the key in my pocket and open the doors and start the car. There's no "nostalgic" lost without having a key.
As for having to jump it if they battery is dead. I feel that the starter is smart enough to keep cranking until the engine is started. The week after I got the car, the temperature was down in the 0's, and noticed one time that the starter cranked for a split second longer than it did previously.
The one thing I didn't like about the push button start, is that I killed the engine once while still backing out of my driveway. I pushed the Start button instead of turning on the radio. But i believe that it won't shut off if you're driving over a certain speed.
Also, with any spare keys, I can set up driving profiles. So that I can limit speed, keep radio off, basically piss off any teenager who may have a chance to drive it. I don't have any kids, so I never thought I would use that feature, until last week.
I dropped my car off at the dealer to get some work done, and noticed that someone took the car down a mile long road for a joyride. I have Automatic.com, and shows me where the car is, and if there was any hard accelerations or braking. And someone had some fun. I wasn't too pleased. So I'm going to program the other key to limit acceleration, for when I drop the car off at any repair places.