I know the final shots are different. In the 1925 version, the Little Tramp is shown smiling with Georgia, and the movie ends with the couple kissing while getting their picture taken by a photographer on the deck of the ship they were on. I read somewhere that the critics of the time didn't like this because they thought a happy ending with the Little Tramp smiling betrayed the lonely poignancy of the character. So perhaps reacting to this criticism, Chaplin cut those final shots out and the 1942 version of the movie ends with the Little Tramp and Georgia heading up the steps to where the photographer has his camera set-up.
Now I actually like Chaplin's narration in the 1942 version and also like that in that version, I can watch the movie without the inter-titles breaking up the visuals by popping up in the middle of scenes. But the ending of the 1925 version is superior simply for being a more fitting, less abrupt ending to the film, and hence I think the 1925 version is the better version of the movie.
And there are also some other cuts and changes within the 1942 version, but I don't know what they all are.
Addition:
The "Cut List" page at the DVDFile site lists the differences between the 1925 and 1942 versions (scroll to the very botton of the page. Note that the write-up calls Chaplin's character "Charlie" instead of the Little Tramp or the Lone Prospector):
http://www.dvdfile.com/software/cut_list/index.html
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