Can a 400BBM w/cheap aluminum heads compete/dominate against the street LS?

LS motors are efficient and the blocks are strong, but they're not huge power makers without a lot of work. The heads seem to flow ~240cfm, TF270 heads flow 340 (600+ HP LS motors are using 350+ cfm aftermarket heads). The bore of the BBM is larger, so more torque right off the bat. The big advantage with LS motors is that there's millions of them, and parts are cheap, proven combos are well known, and the blocks are capable of dealing with immense power/stress.

I can't imagine a 400 with TF270's not having an advantage over an NA LS motor - the BBM wouldn't even need a stupidly huge cam to overpower most NA LS motors. Get a set of 1.7 rocker arms, and the number of advantages of the LS motor shrink further. The BBM likely won't get the MPGs an NA LS motor does, but it should be decent if the cam isn't too huge. With a solid cam, I can't see why you can't spin the 400 to 7-7500 rpm either (with appropriate prep and combination, obviously). With decent compression, 5-600 streetable HP should be attainable with a stock stroke I would imagine (many 451+ CI motors are well over 700 horse).

Whether more stroke or other tricks would be needed would depend on your quarry. If you're just looking to 'keep up' on the freeway and stoplight to stoplight, I think a 400 can be put together for a reasonable amount that can do just that. Being competitive with strip-built LS powered cars is something entirely different (since they're going to have aftermarket heads and cams more often than "LS swapped" junkers). Power-added LS motors are a different beast entirely because the blocks have such immense strength that huge NOS systems and big turbos are not uncommon.