Never used Virgin (although by all accounts Upper Class is somewhat ahead of CX or BA, particularly given the Clubhouses).
Between BA and CX it depends on class and on whether they are flights where you plan to sleep or to stay awake, and how big you are.
In F I would say CX in any case. The service is more consistently good, AVOD on decent screens, caviar (if that's your thing).
In J it's a close call. Probably BA if you want to sleep (truly flat beds) and CX by a fraction for a day flight (less claustrophobic cabin, AVOD). But the BA bed is short - if you are more than 6' tall then you may find it cramped.
BA has WT+, CX doesn't.
In economy, I'd say not much to choose.
If you have OneWorld status then that might make a difference too. There's not much to choose between the BA and CX lounges at LHR, but CX's at HKG (F lounge in particular) are far superior. Of course if you are BA Gold you could use the CX F lounge even if flying BA... OneWorld status in Y would also get you through Zone R at LHR which could save you a bunch of time & stress. (If in J or F then not much to choose since both get ZoneR or FastTrack).