You don't mention class of service but a few general observations--

--VS's strongest feature are its lounges, but fortunately if you are entitled to access them, you get access flying either airline.

--VS A330s have better IFE than VS's older planes, and USB power throughout and AC power in Upper Class (whereas their older planes have only Empower and only in Upper Class). But the A330's business class seats are much more cramped than those of their other aircraft types. Unfortunately the 744, which has Virgin's best business class seats, is going away very soon.

--Service is probably a bit better (and a lot cheekier) on VS, especially in coach, but both are usually good; food may be a bit better on VS in coach, and is probably a bit better in business class on DL though VS's Upper Class catering is certainly not bad.

Also, funny you mention the 764 specifically but for the most part I prefer the 763 on DL, since the 763 has far more entertainment options and, in business class, bigger lavs.