The big sister has to be Faith because previously before the discussion you quoted before Buffy was going to kill Faith to feed her blood to Angel, they had a discussion where this was said:
Faith: Yeah, you know exactly what I'm about because you have it in you too.
Buffy: No Faith, you're sick.
Faith: I've seen it B, you've got the lust. And I'm not just talking about screwing vampires.
Buffy: Don't you dare bring him into this.
Faith: It was good, wasn't it? The sex, the danger. I bet a part of you even dug him when he went psycho.
Buffy: No.
Faith: See, you need me to rely on because you're afraid you'll go over it, aren't you B? You can't handle watching me live it my own way, having a blast because it tempts you. You know it could be you. There's my girl.
First of all Faith is way more matured then Buffy...more let loose..she says that buffy wants to be like her..so she's the big girl..and i'm gonna quote the fight scene...
Buffy: There's a cure.
Faith: Damn. What is it?
Buffy: Your blood. As justice goes, it's not unpoetic, don't you think?
Faith: Come to get me? You gonna feed me to Angel? You know you're not gonna take me alive.
Buffy: Not a problem.
Faith: Well, look at you. All dressed up in big sister's clothes.
Buffy: You told me I was just like you- that I was holding it in.
Faith: Ready to cut loose?
Buffy: Try me.
Faith: Okay then. Give us a kiss.
Look at the bold portion...it is Faith specifiacally talking to Buffy saying to her that she's finally a big girl.