The truth is it really varies for each woman. Some lucky women say that the labor contractions are like an intense version of a menstrual cramp, for others it is the most painful experience of their life. Really it depends on your tolerance for pain. My experience with it was not too bad, i did not really need any pain medications. It was defiantly intense but it was tolerable. A friend of mine on the other hand was screaming at the top of her lungs in agony.
Braxton hicks contractions (false labor) should not be very painful at all and most woman may not even feel them. It is like an intense pressure and a moderate cramp happening at once, and the muscles do not feel like they are pushing just cramping. Labor contractions have a pushing sensation down low and can make you feel like you have to go to the bathroom as well.