The MkIIs are forged frames, but that actually showed to be weaker in the long run compared to the cast MkIIIs. (MkIIIs actually were forged frames for a while, too.)
The biggest difference in the MkIII compared to the MkIIs is that the MkIII has sight dovetails and a reshaped ejection port to eliminate the rare issue of slide cracking.
Later, the MkIIIS came out, with a firing pin safety. It is rumored that some MkIIs had this, I don't know.
Most people, like me, call their MkIIIS's MkIIIs. It's a semantics issue. Regardless, if you buy a BHP made after '94, you will get the stronger cast frame, which will put up with hot loads a lot better.
(FYI: The change to cast frames came when FN was testing the .40 cartridge in the HP. After about 5,000 rounds, the forged frame would warp, and sometimes crack. Cast frames help up a lot better, so they decided to make the 9mms cast as well.)
Forged frames look a little better -- they're "smoother" looking.
IMO, it's a no-brainer to get the stronger frame. YMMV.
Wes