Anna and I had similar conversations after I came out to her. As Reine mentioned, purposefully not referring to Amy in the third person, using personal pronouns like "me" and "I" and "you" ... that small change, made communicating about my gender issues about a thousand times easier.
My emotions are slightly different in my girl mode, and I think that's because I subconsciously "give my self permission" to experiences and feelings I wouldn't normally feel free to have when I'm in that mode. I've been slowly learning to integrate both sides of my personality, and that's been a positive thing so far. It definitely wasn't helpful to think of myself as two personalities. Your mileage may vary of course :-)