I have only seen NYSE specific prop firms, I haven't seen any NASDAQ exclusive.
I believe there are more NYSE stocks that I like to trade, but the few NASDAQ stocks that I like, I trade often. AAPL being a perfect example. Really though, I trade whatever moves. VLO, PD, XOM, NEM, X and all those on the NYSE are fine for me as well.
Some pick only one exchange to trade, some don't really care, I guess you can say I'm the one that doesn't really care.