I know these sorts of threads pop up from time to time, and I'm not sure I've seen one comparing the transatlantic offerings of Delta and BA. This is perhaps more relevant given Delta's relatively recent upgrade to flat bed seating (not to mention the fact that it's a similar hard product to BA/BMI's new mid-haul seating.)

I'll try and keep it fairly succinct and to the point.

Check-In/Bag Drop: The Sky Team Priority Bag drop area was crowded on Sunday morning at 7am, we queued for 5 to 10 minutes to drop our bags. It was much better in Detroit, but still a frustrating process whereby you're not allowed to get a boarding card from a person, but you are forced (sent away from the desk!) to use the machines before coming back to drop bags.
Result: BA WIN Queuing in T5 for this is almost non-existant

Mobile App: I can only compare the iPhone apps. The Delta app lets you check in the whole party that you're travelling with as long as you have your SkyMiles number against your name, whilst the BA one doesn't. Seat selection is also much slicker and easier than the BA app. Keeping track of your points (Avios or SkyMiles) is much better on the BA App though as is flight search and booking.
Result: On balance, this one goes to Delta for ease of use and efficiency with the check-in

Lounges: Mixed bag here, the SkyTeam lounge at Heathrow T4 is excellent, plenty of space, modern and with a good selection of food. It is a J lounge, so I won't compare it to the F product in T5. Up against Galleries I'd say a score draw. They Delta lounge at DTW on the other hand is awful. Yes it's big and showy (it is in the States after all) but the soft product is DIRE. barely a selection of peanuts and some drinks. Diappointing before a 10pm flight when we wanted a "Dine in lounge" option before the red-eye.
Result: BA win. A lot.

On-board Service: Despite the overly familiar nature of the Delta crew, and the fact that they don't even check your boarding pass as you board, let alone direct you/show you to your seat they still win here. My jacket on both sectors was take and hung in the locker before I'd even got my bag in the overhead, as was everyone else's, food orders were taken before take-off consistently and the food was excellent, with very attentive service throughout the flights. This is in contrast to the fairly absent BA service "between feeds" where it's more usual to have to request something than be offered it.
Result: Delta win.

Hard Product: The most important element here, especially given the similarity in set up of the seating with the new BA/BMI mid-haul. Delta's middle seating was awful, utterly terrible. On boarding/take off/landing the seat is too upright, there is no comfortable position, and a quick straw poll of my non-FF colleagues revealed the same opinion. It only got worse as you converted it to a bed. Your feet are expected to "slot" into the armrest/table of the seats in front. My size 12 feet (13 for our US cousins) were 'too tall' for this and had to be at an uncomfortable angle, toes pressed into the roof of the alcove, and my legs were locked together, as I couldn't move my knees apart given the narrow slot, or raise them given the low roof. Naturally this rendered it impossible to get comfortable on my side for example. It's also very narrow at the shoulder to the point where I was touching both sides (and don't forget, unable to turn onto my side). The window seating was a lot better as you're not trapped betweem two seats which means there's a 'cut out' against the wall, but still not really big enough around the legs.
Result: BA win. Delta have provided a coffin to sleep in.

Overall, whilst the soft product is excellent, the hard product is always going to be the deciding factor and the Delta BusinessElite seating being almost universally uncomfortable in any position just can't be overcome by the other plus points here, not for an 8 hour flight. I hope the BA/BMI mid-haul hard product can avoid these space issues, especially if you find yourself in the lone single seat having to squeeze your lower body into the armrest of the seat in front.
Final Result: BA Win.

DTW seems likely to be a new regular route for me, and it's going to have to be Delta given the complete lack of anyone else flying direct from London, and the pricing of other J fare layover routes.