I've done both, in all classes. Pros and cons to both.
Delta.
Pros
J class - good seat if you're travelling by yourself, more private than VA.
J class - Aisle access from every seat.
Better selection in AVOD.
If connecting in LAX, better to arrive in the DL terminal than TB. Also can be less busier (although not always!) Also better arrival time in LAX for connections than VA1.
Cons
Service not comparable to VA in either class.
FA's much grumpier.
J class - catering not near as good.
Cabin a bit more dated and boring.
Virgin.
Pros
J class - better service, catering and of course the self serve bar is a winner.
J class - the fact that they make your bed is a bonus.
If J class is not an option, Y+ is pretty good value for money.
Friendlier cabin crew, better service on the ground.
Cabin design is more modern and in general a better environment.
Cons.
J class - some seats don't have aisle access.
Less individual space, although better if traveling with someone.
Y class - seats are harder.
AVOD whilst a nice interface, has less selection than DL.
Arrival at TB and time of day for VA1 not quite as good for connections.
Overall I think they are comparable products, with slight differences, at least in J. I think VA has a better proposition in Y class, and as a Plat I get better recognition when flying with them so usually stick to the VA1/2 combo when flying in and out of LAX.
Hope this helps.