These two words both indicate people's feeling or knowledge that is attained or learnt from some specific or objects in the external world.Sometimes they are exchangeable,but since there is certain difference in meaning,when being exchanged,the parts stressed are slightly different,and sometimes even unexchangeable in use.
In meaning,
1\when indicating some feeling attained through physical organs,"感到" and "觉得" are exchangeable,but "感到" lays strong emphasis on the organic feeling. EG:我感到/觉得身体不舒服。
2\ "感到" should be used if emphasizing the physical and psychological feelings caused by some objective factor and condition,etc. EG:听到这个消息,我感到很吃惊。
3\If the emphasis is not laid on the feeling attained from some objective factors or conditions, but laid on the individual's view or idea of the objective thing. EG:我觉得你不应该这么做。