This topic potentially calls many generalizations into the thread. At the risk of steering this in a direction you may not want it to go I give you the following to think about.
Many of the larger schools are in larger cities, therefore, closer to soccer clubs and probably have on average more club players on their team. That being said, they would tend to be more experienced players, just due to more time on the field.
What you may in fact be seeing is technically sound hard challenges or tackles in the higher levels, and careless or reckless challenges in the lower levels. Both can and often send the opposing player flying, but correctly done, the hard challenge and tackle will not result in a foul, where as, the careless or reckless challenges result in fouls and cards.
The other posts are valid, play your same physical game and adjust to the game time situation.