LH -
Aircraft are great, new fleets coming in with the 380, the 787 and (possibly) the A350 XWB.
Varied destinations when you are senior enough to bid!
Hotels are excellent. Most city centre and quiet
Rosters are getting tighter but not too tight yet, will have to see when all of the Colgen Air mud settles and the FAA/EASA FTL agreements get hammered out.
Very stable.
SH -
Busy but fun.
Great hotels, great destinations. Most hotels are city centre well away from the airport.
The length of the night stops can run short sometimes. However this can be balanced by standover days and lengthier stops if bid for. Sometimes its just nice to switch the jet off and go look around where you've flown to!
If you get in at the start of a recruitment phase you can gain control of your roster quite quickly and thus your time off and your variable pay.
Very stable.
Is it about money? If that is your primary driver then as you have intimated BA is probably not going to be the thing for you. If it is about variety, the ability to mix SH and LH and the ability to look around the places you fly to then possibly, yes BA could do it for you.
Time to command is a variable feast as NOD states. IF the company expands (bear in mind there is very little space at LHR) then TTC could come down. There has been little movement for the past 5 years mind you which means there are many, many SFO's awaiting their turn which will slow things down for current joiners. The pension changes might be having a fairly dramatic effect at the moment though as those on the top find they can't syphon off excess into AVC's as they used to.
Food for thought.