OK, I ran a quick, unscientific test. I generated a series of maps under Beyond the Sword, and then a series of maps under regular Civ4 (albeit with the most recent patch.) Settings were Pangaea / Large / Temperate, the other settings were the defaults. I then opened up each map in the world editor, saved it out, then went through with a text editor to count the Copper and Horses.
I got roughly the same number of resources in both series of maps--between nine and eleven of each, averaging ten, per map (number of players is eight, so that's slightly more than one per player.) So between default Civ4 and Beyond the Sword, it does appear to generate an equal number of critical resources. I haven't tried unpatched Civ4, too lazy to do so, but it should be easy to reproduce my results.
Interestingly, one map in the Beyond the Sword run had *far* more resources for both--fifteen for Horses and for Copper, which is far more than any of the other maps had for either. I have no idea why, and I was using the "Regenerate Map" option, so there's no possibility that the parameters had changed. It looks like, every once in a while you get a "resource rich" map that just has a lot more of everything--either that, or for whatever reason it had far more landmass, and consequently far more resources.
The one issue I haven't looked at is whether or not critical resources show up in the starting area. The game does look for "good" starting spots, and I think (not sure) that it takes into account resources that the player can't see yet. Actually, that's one variable which, if modified, can greatly affect the perception of availability of resources; if Beyond the Sword only takes into account visible resources, that would result in both Horses and Copper (and Iron, etc.) being more difficult to get. The problem is I can't check this on my maps, as I ran one series under Noble and another under Prince, and the difficulty level affects how favorable the starting area is, so I'd have to run a new series to check, and, well, I'm lazy.
