The scenarios in your OP are a bit too nebulous to really say for sure. They both normally start with clues and leads and such, not just a task with no prior information. Area 51 would obviously favor Bats, though, because he's more equipped for breaking and entering a complex. But that's not really a statement on his detective prowess.
Probably the closest to an answer you can get, without sliding into baseless conjecture, is saying that it depends on the scenario. Holmes is likely better at pure deduction, but certain scenarios would be easier to crack with Batman's tech and/or fighting prowess. I'd venture to say that any opinion beyond that is, at best, unprovable. And at worst, guesswork.