Starting your opponent's WR's QB, or your opponent's QB's WR, reduces the variance in the game. If you're in a 2WR/1TE league, and one team starts Brady/Kennison/S.Parker/Gonzalez and the other one starts T.Green/R.Caldwell/D.Gabriel/B.Watson, those players will more or less cancel each other out, which means the game will be decided based on the difference in RB, K, and D. If you think your RB, K, and D are much stronger, you'd be glad to have this kind of setup; if you think yours are weaker, you'd want to have fewer positions cancelling themselves out.
The effect is fairly small and should only be used on close decisions. Don't sit Marvin Harrison for Samie Parker just because your opponent is starting Green.
If you start Bulger because your opponent started Holt NOT because he's your best QB that's foolish IMO.
It
depends on the situation. A couple of situations (some already mentioned):
1. You are a huge favorite and the only way you will lose is if your opponents only stud goes absolutely wild. If you have to choose between Delhomme (pre-injury) or Hasselbeck and you opponent has a bunch of stiffs along with Steve Smith, then you should start Delhomme. I had this happen to me last week. My opponent, between bad trades and unfortunate injuries, had McGahee, sammy Morris, Bernard Berrian, and Larry Fitzgerald at the skill positions. I had LT, Gore, S. Smith, and Donald Driver. HUGE advantage to me. The only reasonable way I lose is if my guys stink it up and Fitzgerald goes for 170 and 3 TDs. My opitons at QB were Hasselbeck or Leinart. The decision to start Leinart was a no brainer. Now the game basically comes down to my 4 guys against his remaining 3 plus his QB (Delhomme who I've also partially cancelled out with Smith).