It depends on both the AAA and Modern Rock station. For instance in Indy, our AAA WTTS, and our Alternative WRZX have little or no cross over records, Maybe R.E.M, thats it.
Our AAA share's more of its playlist with our Classic Rocker WFBQ.
There is a pretty good station in Cincinatti called WOXY, its a net only station, but it used to be on 97.7 with a weak rimshot signal, it was called 97x until the fm went away a few years ago. Anyway WOXY always has played the more adult and indie Alt Rock bands, so im sure stations like WOXY and Indie 103.1 in L.A share some songs with (SOME) Triple As.
Most of the overlap with Alternative comes from Active Rock, the two formats are almost identical now days, still there is a difference cause Active Rock mixes in Classic Hard Rock, stuff like Motley Crue and AC-DC, instead of classic's from the ALT format like THE CLASH, The Cure, DEPECHE MODE, Talking Heads, Ramones etc...... Our AAA will play classic Alternative from the above bands, but our ALT Rocker sticks to new music, and 90s grunge. I guess their is some crossover when you count the classic's.