Buy 'em both...
Yes, I know that this is the generic response, but it's nice to have both!
Now, since you are apparently looking for only one (at this time), here are my pros and cons about each pistol:
Sig P226
Pros:
15+1 capacity
Very accurate
Reliable with almost any 9 mm load you want to shove through it, from underpowered subsonic plinking loads, all the way to hot NATO-spec ammo.
15 round factory magazines are plentiful, but somewhat expensive (50-60 bucks)
Cons:
Double stack magazine gives this pistol handle a rather wide grip that smaller handed people may not like
The K-Kote version seems to have rusting problems; stick with the Nitron finish.
Costs about 100-200 bucks more than the BHP.
Not really ideal for concealed carry purposes.
BHP:
Pros:
13+1 capacity
13 round factory magazines are extremely plentiful
17 round South African magazines are also plentiful and cheap, and work well.
Grip is very ergonomically designed. It just "feels" like it was made for the human hand.
Has just a wee bit more accuracy than the Sig P226
Despite the 13+1 capacity, the grip is very slim, and those with smaller hands may find that they would enjoy this gun much more.
Slim, flat profile actually makes this gun suitable for concealed carry purposes, despite its 5" barrel. Get the correct holster, though...
Browning told S&W and the KGB (Klinton Gore Bunch) to sick their agreement where the sun doesn't shine...
Cons:
Unless you have one that was made in Portugal, you may find that the BHP is somewhat finicky about the ammunition that it can feed. Test it thoroughly.