AFAICT, the Yardbirds would be more polite but very versatile, and the BG50 a bit more beefy.
Yep, that's exactly what I'd say...
My BG50s are in ash body, maple boards.
My Yardbirds are in an alder body, rosewood board.
At some point, I might try swapping them about to see what they do in other combinations - but that's not going to happen in the near future.
My gut feeling is I'd stick Yardbirds in yours if it was mine... :D