I think Faith was truly trying to be helpful, but she sort of blundered the whole situation. As the "other Slayer," she should have had some sort of authority (in fact said outside the Bronze, "I expect you to look out for these girls..." or something to that effect, which is a clear indication that she had every intention of sharing her authority, at least to some extent, with her sister Slayer. The only real leadership experience that faith had ever had was in the 3 episodes of Angel prior to returning to Sunnydale, and she had no problem whatsoever to letting Buffy bear the load of leader while she herself more or less played high ranking muscle.
Her mistake was in not, after Buffy announced her plans to return to the vineyard, asking Buffy to join her privately in the kitchen where they could work out an alternate plan, possibly involving a smaller force scouting out the situation before launching a full force assault. Unfortunately, her timing was bad and Giles, still stung by Buffy's choosing Spike's welfare over his own judgment, leaped at the opportunity to re-establish his influence. Xander, probably still doped up from his stay in the hospital, and Willow, hurt because Buffy hadn't stayed with her by Xander's side were no support whatsoever, and self proclaimed brat Kennedy only added fuel to the fire.
Buffy's mistake was in ever showing any weakness in the situation at all. "Look, I'm willing to discuss strategy..." should have been more like, "I'm the one in charge here, and if you don't like it, then haul your a**es out of here. We've got a war to fight, and if you don't want to help, then don't hinder." The biggets betrayal in the whole thing was her own sister. If Dawn had been at least slightly supportive, things might have been different, and the situation might have been contained. With no allies whatsoever Buffy saw only two options: stay and possibly have the situation degenerate into violence, or leave. What she SHOULD have done was to take a note from Travis at the Alamo. Draw a line and invite anyone willing to fight to the bitter end to join her and whoever didn't would be free to leave.
With Buffy leaving, Faith had no choice in the matter. She HAD to stay, since she was the one most taking Buffy's place and getting the job done. I find it both interesting and completely appropriate that Faith was the one who followed her outside and not any of her other friends. It was also significant that Buffy gave her advice rather than attacking her, either verbally or physically, and telling her not to be afraid to lead the others. Was that a warning for Faith, a reminder that she, now, was the only one capable of holding the group together?
Regardless of anything else, I think Faith did the only thing that she could do, once the whole thing started, and that was to fill the vacuum left by Buffy's leaving. (Besides, it gave Buffy and Spike a little private snuggle time before the big battle.)
