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.
Both exchanges are easy to lose money. If you have full time and want a fast action then trade on NASD. Otherwise, trade on NYSE and it's good for you to learn how to trade stocks as well. The most reliable and less manipulation (trapped) is NYSE. I think most institutions prefer NYSE and it's the king of the world most reputable exchanges.
In my experience when you get into NYSE or NASDAQ it depends on the 'strategy' that their top traders use and which they might push on newbies, like scalping NYSE for a few cents. In that case they might even discourage NASDAQ unless you got experience or put up the risk capital. So it depends on you more than them. GL http://tequity.blogspot.com