Apologies if this was ask previously, but I am unable to find an answer

I am planning a trip from JFK to LHR. Does it matter if I fly on a DL flight or a code share with Virgin?
Last year, I obtained Platinum Medallion status, so I assume I will be in "Economy Delight" if I fly on Virgin equipment

All things being equal, is there a benefit of flying Delta equipment vs Virgin equipment?

Thanks

Dopey