Simply, it's NOT the same, but the differences could be very minor or could be enough to cause damage to something.
The limited data I have from snooping into VW engines, says both BMB and BLY are EU2 emmisions, have map-controlled cooling, no , 10.5:1 compression , no NOX storage, no Secondary Air, have VVT, and are manual trans (as you say). The BMB finished on the same date that the BLY took over.
It *MAY* be as little as a different software version, or it could be a different number of lambda probes - they DO use different exhaust manifolds - I suspect this as a difference, check the donor for the number of probes. I KNOW the BLY has 2 lamba probes (pre cat, post cat, and has a 4into1 manifold and cat, with a single "downpipe"), I STRONGLY suspect the BMB used 2x 2into1 manifolds, 2 cats and 4 lambda probes (and possibly another further down, after the 2 pipes join, but prolly not), with 2 downpies that join under the car. If this is so, you can also swap the exhaust and lambdas with the additiona wiring or swap that part of the loom.
It could be the SAME physical engine, but with slight other wiring differences too.
You can download the wiring diagrams with an
ErWin account, and check for differences.
There will ALWAYS be a risk involved, but if it were me, I'd do it anyway, aftyer checking the exhaust and wiring... but I'd work out how to fix what I screwed up too, if that happened - so obviously the risk is all yours :-)
Worst case is you smoke something, but your best case right now is a car that doesn't go at all.
Good luck