What is making you shy away from the B16?
Sure the H makes more power, but you have much less aftermarket support.. that damn autotensioner, pick up some pricey mounts and the swap is more difficult. You have to deal w/the shift linkage etc.. amongst other things I'm sure I'm forgetting.
..Is it a big deal, no. But it's more to deal w/regardless.
Eventhough the H isn't significantly heavier than the B. The motor wasn't designed to go in that bay, so the weight distribution in the car will be different. Whether or not the H swapped vehicle's distribution would be better or worse, I cannot comment for sure, but I'm leaning toward the latter statement..
From my experience it seems like the H swap sits more toward the front of the vehicle and wasn't centralized in the bay (from side to side) which is something you would not want from a handling standpoint.
All these things are minor details, and probobly would not be too noticeable on lap times but it's something to consider.
The H is a great swap, don't get me wrong. I have a friend w/this swap, and that car has torque for days.. But I personally would stick w/the B-series and enjoy a wide variety of aftermarket parts, and a somewhat headache free swap
The LS is another great option, but only if it's boosted.. the question you have to ask is if you have the time/resources/knowledge to actually make it there. I think you'd end up being dissapointed in the LS in NA form..
You know you can afford the B16, and it already offers decent power in stock form...