From what I understand, the faces impact a few things. Those with a happier face are more likely to jump out of the back-ground to help you if you get caught in multi-hitting grabs, combos, etc. It also affects super meter from round to round. If a character gets knocked out and the next character in line had a happy face, I think they may gain a meter stock or something along those lines. The feature was removed in 98 UM, though.
Like I said though, I'm not 100% positive on that; if I am wrong on some aspect please feel free to correct me.