Even though A Link to the Past is an amazing game and my #5 favorite Zelda game, it's handheld counterpart Link's Awakening is obviously superior as it trounces it's 'big brother' in every possible way and even did more, besides maybe, graphics which is a given considering. Link's Awakening, a brilliant and extremely underrated game in my opinion, is my #2 Zelda game an my #5 'best game ever made'.
Sadly I reckon Link's Awakening will lose this solely due to it being overlooked, lesser well known and due to people assuming the SNES game is better just because of it's reputation. I feel Yoshi's Island suffers a similar fate all the time against it's inferior predecessor.
If I have to choose which is the lesser (I won't say 'worse') of the two, I'd choose, A Link to the Past.