Having both apps on the same phone may cause presence for that phone to be unreliable. Other than that, there are quite a few people who have run both versions of the app for awhile.
If you use smart home monitor in the classic app you also need to be aware that it is completely different code from smartthings home monitor in the new app, so you can’t dismiss notifications from one in the other. See the community FAQ:
FAQ: SHM and STHM are different
Finally, one issue to be aware of is that you may not have enough Z wave or zigbee repeaters to have a good networks on both hubs. This can be tricky to balance. As you remove devices which are repeaters from your V1 hub, that network efficiency will go down and some devices might even become unreachable. And as you slowly add devices which are repeaters to your V3 hub, you may not have enough repeaters there at the beginning.
So this is just something to be aware of as you start moving devices over.