I'm stuck between these also.
MVP can be vaped while charging, Groove can't, at least the original plastic ones can't. I'll search more, but pretty sure the new SS Groove can't vape while charging.
Groove's 3800 mAhs should always last me eventhough I dry burn my coil about every 3ml, but I like the assurance of the MVP being a PT I can connect to my car or wall and never worry about battery life usually, but again 3800 mAhs is a lot and requires no car adapter & wire.
Groove has an ohm meter, MVP doesn't, but I just wrap 4X and know my general ohms. Where I set my volts is most important and basically overrides needing to know the ohm.
I presonally don't need the Variable Wattage of the Groove, which MVP doesn't have.
Groove can't scroll volts/watts, but it round robins. MVP doesn't round robin and I'm pretty sure it scrolls, but MVP has a basically useless puff counter you must bypass that might be as much work as tapping + or - volt/watt on the Groove.
Groove is thinner, but wider and taller. But if you use a 510 tank, you're height will be less than the MVP because MVP has the EGO + 510 adapter that sticks out. I use a 510 Protank, and would just get a $3 510-to-ego adapter if ever needed with the Groove, but I probably won't need EGO threads.
MVP can charge other devices, but I'll probably never need it or be carrying a wire when I do.
I think MVP's easier to fire from where the button is.
Despite Groove being SS, I'm pretty sure MVP's built stronger.
Pbusardo review of Groove w/ MVP comparisons:
A PBusardo Review - The Smoktech Groove - YouTube
People commented that their fire button doesn't stick like the one in Pbusardo's review.