Check your rim strip, make sure it's centered and covering your nipples(that sounds bad), check the inside of your tires for hidden broken off spurs/thorns/glass ect. What pressure do you run, over/underinflation can lead to flats. Get new tubes.
I've replaced the rim strips, and tried different sets of tires, as well as had the bike shop go through them....nothing. The flats I'm getting are pinch flats from me losing air. If I ride on the street or smooth trails then they hold well, but when I'm hitting some ruff stuff they leak out with each hit. I'm going through a tube every 4-5 rides now and I'm tired of replacing them. When I ran schrader valves I went almost a year before my first flat. I don't check my pressure, I've always gone by feel and I know the exact amount of sag I need to ride like I do.
I prefer presta because I've had much better luck with getting pump valve heads to lock and stay on. Schrader is a pain because you have to push it down to open the little pin valve and lock it just right.
Really, both are perfectly adequate for most cases. Schrader will be more difficult at high pressures. Presta will be harder to find a pump if you forget yours and don't have an adapter handy.
I've never had a issue pumping up schraders, I do have trouble sometimes pumping up the prestas becuase I have to use an adapter. Everyone I ride with uses schraders so I keep my pump set up for them. When I use the adapter for my valves sometimes when I take the pump off the valves stay open and leak down the tire, which is another reason I'd like to get rid of them.
I'm thinking for skinnier rims and tires with higher pressure they would be great, but I just can't seem to get them to work for me as is.
PS I'm running velocity rims, I chose them cause they are thicker and a little more heavy duty so drilling them won't compromise the stregnth.