Not so fast my friends! If you don't smell the similarity, then you don't and that's the end of that, but I'm'a try and back up what I'm saying for the sake of conversation. Don't do the comparison from memory, spray them both on cards or something; memories aren't the most accurate things. Now, there's no note breakdown for BA, but there is one for OI and I think they've both got oud, wood (likely sandal wood in BA certainly sandal wood in OI) and patchouli, and OI has labdanum for sure. I'm not positive BA has labdanum as its one of those scents that's kind of hard for me to pick out specifically but here's a nice description written by Sculpture of Soul (he's not talking about BA, but labdanum specifically) that makes me think it does: "warm, kind of leathery scent with hints of pepper, tar, coffee, light tobacco, etc, while not really smelling just like any one of them." That description leads me to believe BA has got labdanum, if not it has several of the things that comprise the smell of labdanum, leaving Rose to be the only note that OI has that BA likely doesn't.
For what it's worth approximately 22 hours later, after a shower, reapplication of another frag, going out, reapplication of another frag and sleep, I can still smell the one spray of Oud Ispahan on my arm! This stuff has got longevity in spades if nothing else.