I can only tell you what I think and what I have done with the Push in the last four days.
Studio or performance tool?
I would say both. The strengths of Push (or the strengths of the Push concept) are clearly in the creation phase. It’s very fast, even faster if you have a few things in mind beforehand.
Performing is of course also great, but you might want to have an extra controller (Faderfox etc) on the side, as some functions are not always directly controllable from push; mixer volume vs device control, for example, are not accessible at the same time on an encoder page.
What push doesn’t do well is everything in between. But everyone has their own view on that, so I’ll save that for now. But things like highly complex arranging, automation data editing etc. are not found on Push and I think most of it makes more sense on a DAW.
UI
About the UI snappines, I can only tell you that it actually runs well, but sometimes it definitely comes to the one or other dropouts. I don’t mean the audio at all but actually the UI. So compared to the M+ is the Push 3 not so snappi. But most of the time it doesn’t bother me. We’re talking about a few nano seconds.
Mute/unmute I like better on the M+. But this is due to the layout of the buttons on the Push, no idea why they have made a thick poti (tempo) under the buttons, which disturbs a little. In addition, you always have to exert a decent pressure on the push to trigger the buttons. But all in all, the function is similar.
Timestretching
Is pure gold with the Push, no comparison to the M+. This is a completely different league.
Ableton Live is simply better at the core in terms of working with audi, but to see the whole thing in standalone is very impressive.
(Almost) Everything you know from Live with clips also works on the Push 3. As an example take my session from Saturday. I sampled whole vinyls into the Push, so whole tracks (7min+) from start to finish. On the Push you can edit the audioclip, select the 1st downbeat with the JogWheel and then warp it with the grid. Takes a few seconds. And this usually runs directly in sync with the project.
I ended up with 20 tracks in the set, all running with “complex” warp algos. That didn’t jolt the push. But what is very fast with it, is to empty the battery.
I did this all with 44100. So no idea how it behaves at higher sample rates.