All things being equal, the flat jon will need less water. For what you're describing, I would definitely get a flat bottom jon boat. I have a 16' flat jon and I love it. You can get into pretty shallow areas with it.
My main concern is that one of the rivers I am going to be fishing is very shallow in some spots, as in like 6 inches and I'm not sure if I could get a v bottom through that. This river doesn't have a boat launch either.
When you get that shallow, you will have to lift the motor anyway. Then depending on current you can use oars to push you through or Waders/boot to get through.