This question is very well covered in the article at our site that you can find here: http://www.cabling-design.com/editorials/fiber1.shtml
Simply put, 50/125 minron fiber has more bandwidth allowance since due to its smaller core. However, 62.5/125 has less energy loss while launching the signal (bigger core collects more light energy). So all the pros and contras are actually balancing between the two characteristics (plus some more of course). Please read the article for the better explanations.
Dmitri Abaimov, RCDD