Jeez, that would have been a disaster...
But seriously, it would be interesting to see. I'm assuming that in this scenario Faith gets called instead of Buffy (because the only reason Faith gets called to be a Slayer in the first place is because The Master kills Buffy in Sunnydale, which probably wouldn't have happened had she gone to Cleveland or somewhere), in which case Buffy stays at Hemory in L.A.
Thing is, Faith wasn't ready, not even close to ready, to be the Slayer. I mean, okay, no one is "ready" to take on something that massive, not even Buffy, but Faith, until pretty much Angel S4, was a complete mess. She'd been abused and abandoned her entire life, and was so desperate to latch onto someone, anyone, who cared for her that as soon as things soured with her and Buffy she was taken in by The Mayor, a totally evil (albeit very funny) guy. Faith had already dropped out of school by the time she showed up, so I don't think she would have lasted long, or gone at all, at Sunnydale High. And Buffy only really befriends Willow and Xander because she's a good and decent person (remember, she hooks up with Cordy first). Faith wasn't, not at that time, so I don't think she would have teamed up with them.
She probably would have linked up with Giles at some point. I don't think they would have had the chemistry him and Buffy had, at all, but they would have been effective enough. I don't think Giles would have cared for her like he did Buffy though.
All the prophecies that Angel heard from Whistler surrounded Buffy, so Angel probably would have hung around her in L.A. until Faith died (which, being honest here, would most likely have been pretty quick). That means that Angel doesn't go to Sunnydale. Faith probably stops The Master from rising at The Harvest (Luke was pretty dumb), but Angel isn't there to stake Darla. He doesn't become Angelus, but looking long term that means he doesn't do all he does on his own series either. So Cordy gets killed by Russel Winters, Fred stays trapped in Pylea and Gunn eventually gets killed by vampires in his gang while Lorne stays at Karatos. I don't even know about Wes.
With no Angel, and Darla still around, I'm betting The Master probably kills Faith and rises. If Faith manages to get through him, I think she would have had her hands very full with Spike next season.