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.

+1 to PaulR

But maybe you didn't give enough information to get the best advice. I think the P310 and the J1 have a very useful feature that the V1 doesn't: a snapshot flash. The J1 (and V1) has a useful feature the P310 doesn't have: interchangeable lenses. But the P310 has the advantage of a fast lens for low light. And the V1 (which you didn't ask about) has a very useful feature that the other 2 do not have: a viewfinder.

If you have Nikkor lenses for your full frame camera or DX camera, go with the J1, I suppose. I use the V1 and D800, and they are both great. It cracks people up when I load the 70-200 AF-S or my old manual focus 85 mm onto the V1, but the pictures are awesome. I think if you use a long lens with the J1 you will want to use VR lenses or a tripod, because holding the J1 steady will be hard. That's where the V1 would be a better choice: you have a viewfinder: you can push the camera onto your face for stability. Since you are an intermediate photographer, you really want a view finder, so take a close look at the V1 before you decide the J1 is the way you want to go.

Video is great on the V1. I have not bothered with the video on the D800 yet.

You asked about useful features, but there are two useless features on the J1 and V1: "motion snapshot" and "smart photo selector". I keep a piece of gaffers tape over the select dial so I don't accidentally go into one of those modes.

Keep in mind that not everyone likes the Nikon 1 CX format, so you may hear bad things from the self-appointed cognoscenti, who probably have never used the J1 or V1. Still, for the price, it is a step up from the coolpix sensor.

Can only advice on the V1 great camera, viewfinder essential plus with adapter choice of Nikon lenses from your Full Frame camera

The video is excellent and slow motion great, other camera is a D3X but using the V1 most of the time ! Its just a lot lot lighter and unless you are wanting large prints A3+ the V1 is fine

I'd like some advice if you'd be so kind to give it.

Nikon P310
Or
Nikon J1 (10-30mm kit)

-The J1 is $80 cheaper. (though I don't consider that a game changer)
-It will be mainly used by my wife that will most likely have it in auto full time and by me (dslr beginner/intermediate student) when I don't want to carry my full frame.
-Size and weight are not a problem.

I'd just like to know which takes superior photos and has the best "useful" features.