Gene finds comfort in putting on Finny's clothes because for a little while he can be someone other than himself. Because of Gene's guilt and self-loathing, just being himself is painful. Finny is still in the infirmary, and Gene has yet to face him after making him fall from the tree. Gene lives in fear and dread of that moment. No one seems to suspect Gene, but Gene believes that Finny knows. The weight of all his emotions makes Gene's life almost intolerable. After wearing Finny's clothes all evening, Gene sleeps well. When morning comes, however, Gene must once again deal with reality: "[I]t was only on waking up that this illusion was gone, and I was confronted with myself, and what I had done to Finny."
There are a couple of reasons why the clothing comforts Gene. First, he is far more humble and quiet than Finny is, and wishes he sometimes exuded the confidence and waggish ways of Finny himself. By assuming the clothing, Gene feels that he more easily possesses those traits he finds admirable in Finny.
Also, it is comforting to Gene to wear the clothing of Finny since he still feels responsible for the accident on the tree branch. It seems a bit like a way of honoring him, and that is why he finds contentment in the clothing choice.