Well... there's not much choice of OW airlines flying out of HAM to a variety of 'global' destinations: it's either AB or BA/IB.
As for lounge access - OW is very straightforward here: Lounge access is available from the OW sapphire tier onwards which generally needs 50k status miles (or 600 TPs on BA, which is roughly equivalent) annually to attain no matter the program.

As you said that upgrades are important to you - keep in mind that upgrade instruments generally are limited to the issuing program's metal flights.
Of these two, only BA is a truly global airline while AB only has a few longhaul destinations in North America which get serviced with their own metal. For everything else, they rely on codeshares with either EY or OW partners, and these cannot be upgraded with AB instruments.
Should you primarily fly to North or Central America, AA would be another good option to go with. They charge co-pays (USD 700 return) for mileage upgrades, though.
While IB shares much of their program rules with BA, there's one major difference between the two: You can only upgrade full-fare (Y,B,H) IB tickets with Avios, which severely limits the usefulness of it for upgrades.

Also, keep in mind the points expiration policies - as you cannot choose airlines and have no way of predicting which one you'll end up on on work trips, I'd stay away from programs with fixed expiration policies and go with a more generous one. Here, BA with its any-activity-in-36-months policy handily wins.

Taken all this, I'd go with BA.