With simple sentences such as these it is difficult to differentiate the two because both tell you that he felt something in the past.
The main difference is how accurately that point in time can be specified. You can use the simple past to say "He felt something five minutes ago", but the present perfect "He has felt something" only indicates some time before now, and you can't specify exactly when. You can even use the present perfect in a sentence like "He has felt something (sad, say) all his life" to indicate continuity of state over a time frame that stretches to now. This is closer to the meaning of "Ele tem sentido triste" I believe.
I think this example highlights one of the major differences in Portuguese and English to me - I've had barely 5 months of studying here only and could get it totally wrong.
Portuguese does not seem to distinguish between past and present perfect as English does. If you grow up with one language and not the other you might react as we do here: why were you saying the same things on the one hand, and which one is it that you meant on the other ...
English present perfect only emphasizes the fact that the action is complete now: i.e. you have already felt it, and when you did is of no interest or consequence; whereas past tense only tells you that the act happened in the past and strictly speaking does not necessarily, certainly not explicitly, tell you what the connection of that act with the present time (i.e. you have to infer at your own peril - you felt drunk [yesterday] and can drive to work now;? or you have felt drunk [now of course] then you should not drive ). With sufficient context there should be no confusion, or the speaker should provide sufficient qualification to clarify, otherwise there may be no need to make the distinction.