If Asia and Europe are your main markets I would stay with Accor who offer a wide footprint of hotels at all levels (budget to luxury) in those areas. It is probably fair to say that Accor has some of the most stunning properties in Asia. Yes in the US you will only find some Sofitels and one Novotel but it always pays to have a backup programme (I use Hilton for that purpose).

The Le Club Accorhotels programme recently got a facelift with improved perks and unlike the other hotel programmes is incredibly simple (it works on a cash back basis) with no restrictions on premium rooms or blackout dates (except in some very rare instances).