Both have the same meaning, while the former is a little bit more formal than the latter, so you may use the former more in written Chinese and the latter more in spoken Chinese.
February 9, 2012
感觉在Daily Conversation中会用的多一点。如果在一个很casual的背景下，经常用认为会让别人觉得你sanctimonious假正经或者too much powerful.
February 13, 2012
认为:to express their views,tone formal;it's equal to "think".
觉得:to express their feelings,tone casual;it's equal to "feel".
In general, they are universal, and Chinese take no particular attention to this point.