Stefan is way to nice-nice with Elena! He needs to be himself around her otherwise it is fake and everyone knows a fake relationship never ever works out well. Whenever Elena is around Damon she is happy and Damon isn't afraid to be himself around her. Sure they (Damon and Elena) have had their ups and downs, but they always manage to work it out in the end which proves that their relationship is much stronger than Stefan and Elena's! Stefan never tells Elena not to something, especially when she shouldn't do it. Damon would make sure that Elena would not do anything that could get her hurt.
Another reason is that Stefan can't control himself, he is a danger to the people around him because آپ never know when he will go off the rails and hurt someone. Damon does get mad and does stupid stuff, but he would never hurt Elena, no matter what!