It really depends. Nowadays you can get longbows with recurve grips and vice versa. But usually the older bows were made a little different. And personally I like the differences.

Personally, I grip my longbows with my palm pointing upward and the center of pressure of the bow on the lower portion of the palm. Try doing this, put your bow arm in a position parallel to the floor, put your thumb in a position pointing straight up. Relax your bow hand. Now make a fist with your draw hand and try pushing the bow hand at the lower part of the palm. I bet your wrist won't move, just the whole arm. That is kind how how I grip a longbow. Now the recurve, leave your bow arm parellel to the floor again, now keep your thumb and index finger paralell to the floor also. But a slightly bending down force in your wrist (just a little), and relax the hand. Now make a fist with your draw hand, put it in the "V" formed from your thumb and index finger on your bow hand, push hard with your draw hand. Again, not much give in the wrist.

Check out these two arcticles, they are pretty informative:

http://homepage.ntlworld.com/joetapley/stabs.htm

http://www.bowshow.com/artsci.htm