I’ve used it three ways so far. The first is as a controller, same as push 2, but with more fun playing Auras and other MPE enabled stuff.
The most fun way has been as a standalone jam box. I spent a day creating a new set, hitting save immediately, seeing what the set got automatically named and then using that for inspiration. Last one was “Eagle from the sea” so I got the Apollo 11 audio and chopped that up over some drums and a baseline. Have not made more than an 8 bar loop but made more of them than I have in the year so far after getting the push 3. Absolutely a great way to lose yourself for a couple of hours and generate some ideas. The capture midi button is one of those small things that actually make a huge difference as you can quickly grab those happy accidents without breaking flow.
The last way is as a controller/sequencer/tape machine for a few hardware synths I have. Have them connected to ADAT and a mioXL so can hook the Push 3 in and sequence and record them all at once.
It is expensive, and there are lots of things to come, things that aren’t polished, buggy etc. as documented in this thread but I’m still super happy with mine. I am probably square in the target market as some of my favourite times have been getting lost tweaking Wavetable on the Push 2 so this feels like a natural extension.
I made a spreadsheet of the things I’m going to be happy to sell now and they will come to about the same price as the Push 3 cost me so I actually think it’s good value for the enjoyment I’m getting from it.