I would say that this is mostly a lot of noise with very little bona fide content. The two schools have enjoyed similar rankings over the years, although in the ten BusinessWeek rankings to date UCLA had the higher rank 8 times.

UCLA has tended to have the more stable rank overall, trading in a relatively narrow range bounded by 9 and 16. In contrast, UCB has tended to have the more volatile rank, ranging from 8 to 19 and jumping 17 to 8 in just one year (but it also jumped from 19 to 13 in one year and drifted back up to 18 in two ranking events).

1988 UCLA 16, UCB 17
1990 UCLA 10, UCB 19
1992 UCLA 16, UCB 18
1994 UCLA 9, UCB 19
1996 UCLA 12, UCB 13
1998 UCLA 12, UCB 16
2000 UCLA 12, UCB 18
2002 UCB 13, UCLA 16
2004 UCLA 14, UCB 17
2006 UCB 8, UCLA 12

The one bit of true content in the rankings is that Haas enjoyed the arrival dynamic new leader, Dean Campbell, in 2002. Campbell has provided visibility to Haas that Anderson did not really match.

I've heard the argument that UCLA and UCB not so much contenders for the throne of "best University of California campus" as they are educational capitals of two different parts of the state. In this sense UCLA is lucky- it is basically the undisputed leader in the southern part of the state while Berkeley is outclassed by Stanford in the northern part of the state.