In my opinion, I think Adele is the better singer. I love her vocal range, her lyrical skills are superb, and quite frankly I think she is a breath of fresh air for Pop music...at least around here.
As for Lady Gaga...where do I even start? When I first heard of her in my freshman year of college back in 2006, I gave her a shot. At best, I found her..."okay". Over time though, I felt like her songs had become less genuine and that she was more for the over the top imagery than she was for the music. That, and her obsession with shock value is well overused, boring and is looking more attention whore-ish than it is making a statement. Hell, even Todd in the Shadows couldn't have worded it any better in his 'Alejandro' review when he said her shock value "was going the route of Marilyn Manson. It used to be shocking, now it is just cute."