Flying V has easier turn initiation, and if you want to do surfy type things, e.g surfy/skatey moves on the sloped side of a trail, or buttering and spins the flying V board will sort of spin on the rockered centre more easily than the cambered version which will carve more so that spin. It's more 'fun' in concept.
On an icy day the flying V board won't have as much edge hold, and I find that on days where there is a lot of crud the flying V shape kind of bounces off the tops of bumpy stuff while the cambered shape will cut through it or ride through it better. Camber has more pop, better edge hold, is more precise, and a bit easier to catch an edge.
If it's rarely icy where you ride the flying V shape is fine, and keeping it sharp for icy days improves performance a lot.
I have both, and what I find is that on days where I misread the conditions and take the cambered board when it's soft enough for the flying V minor regrets, I have missed out on a little fun, while the days where I expect soft snow and end up with ice I really wish for camber, and may return to the car to swap boards. This is what happens here in Ontario. On a trip out west unless conditions are very unusual I'm on the flying V board most days.
if you can demo or borrow pretty much any flying V board you'll get a sense of it very quickly, and it's really best to ride it, it's a personal preference thing combined with the influence of the conditions.