J1 will smoke the 310 in good light. Especially if you are taking pictures of anything moving. the delay between when you press the shutter button and when your camera focuses and snaps a shot is simply to long for my taste on the P&S cameras. The J1's autofocus puts my D40 SLR to shame, and gives the D90 a run for its money.
Also worth mentioning is shooting speed. I didn't appreciate this until I went to Isla Mujeres for vacation and Carnival was going on. Every neighborhood puts on these crazy dance acts on the main road on the island. Getting the right shot with a P&S would be impossible, but when we dropped the V1 into burst mode (up to 10 FPS) it really shines.
I don't know the P310 very well, but the specs say it has a f1.8 lens, which is faster than any of the Nikon1 lenses, so it might have an edge at base ISO in low light. But I expect the J1 will have superior high ISO quality so that's pretty much a wash.
If you can afford the V1, its a better option than the J1 because of the excellent viewfinder (being able to review shots in the viewfinder is an added bonus as I hate it when people look at my shots while I'm shooting. Of course with the V1 you have to shell out more for the camera and then even more for the separate (but much better) flash.
I also can't recommend the handling of the V1\J1 enough. SLR veterans will balk at having to use the menu to get to ISO settings, but the menu is very responsive, and I actually really like the rocker knob for setting aperture \ shutter speed. And it's great for zooming in on image review.
If you can deal with its eccentricities, the Nikon 1 series gives you awesome shooting performance in a small package at a reasonable price.