First, let me extend a warm FT welcome to you from another Washingtonian who made the move over to London a few years ago.
My advice, if you're flying over 100K miles, would be to avoid both the BA and BD programs, particularly if you're a Y flyer and would like the chance to upgrade to C/F.
Your big choice from London is which alliance you wish to be part of -- StarAlliance or OneWorld. As a Y flyer, I'd recommend AA's program if you decide to go OneWorld and UA's program if you decide to go *A. There are benefits and drawbacks to each.
For what it's worth, I prefer BD's service to BA's, plus as a European UA MP member, I get a free Red Carpet Club membership.