Without a doubt, Buffy and her team did it right, and for the proper reasons. They were stopping the army of the First Evil from overrunning the world, and they pretty much accomplished that, at least as far as the ubervamps were concerned, and, with Caleb's death, the Bringers were left pretty much leaderless, at least until a new general could be recruited and conditioned (assuming, of course, that Caleb was the commander of all of the Bringer forces) Buffy's team stopped the First Evil from escaping the hellmouth, and, as we saw by the events of Dark Horse's Season 8, there were long lasting results from her actions.
Angel's team, I'm not so sure. What they did to the Senior Partners seemed more of a gesture of defiance, and a most likely suicidal one at that, than any sort of plan aimed at actually stopping any plans that they might have had. Yes, they killed all of the members of the Circle Of The Black Thorn, which apparently served as the Senior Partners' Board Of Directors for the world, but that didn't in any way stop what they were capable of doing, as was illustrated by the army of demons in the alley and the act of sending the entire Los Angeles area and its entire population to hell, as we saw later on IDE's "After The Fall" arc. Angel might have caused the Senior Partners to act prematurely on plans that they already had in place, but they were still able to act.
On the other hand...
Would the fact that the Senior Partners apparently left Earth at the end of IDE's final Spike miniseries count as an eventual victory for Angel's team? If so, then it might be argued that Angel set in motion a chain of events that culminated in what might be interpreted as the success of his plan.
Ultimately, the results of the 2 battles were that Buffy and her team pretty much stopped the First Evil and its plans to take over the world, whereas Angel just manager to stir the Senior Partners up enough to make them send a whole bunch of noncombatants to hell a bit sooner than they had originally planned to do.
