The big issue is size - physical external size. The Cobra is a small car, and will swallow a Lima or FE motor without much difficulty. But changing spark plugs can be a nightmare with such limited access.
A secondary issue is parts availability. Just about every kit maker can easily supply parts like motor mounts, trans mounts, headers, etc, for a Windsor motor. They're inexpensive and sitting on the shelf waiting for your call.
Big block parts are not nearly as common, and therefore not nearly as cheap. Some kit makers do not have motor mounts or headers for a BB. You'll have to source them from somewhere else of build them yourself.
Speaking of headers, the exhaust can sometimes be a problem. When you find an off the shelf header, it might not be able to handle 700+hp - you need big tubes and pipes for that.
For economics and ease of maintenance, the small block 408 wins hand down. For ultimate power, bigger is better. You have to decide what you can live with and without, and what you're willing to pay for.
IMO, decide which one gives you a woody. Buy that one.
As for the carb, again it's your choice. I think if you want a nasty engine that screams like a banshee, is easy to drive, and gets good mileage, you need EFI. If the choice is a carb'ed BB vs. EFI 408, I'd take the 408 without a second thought.