I like them both, but I had to go with Quadrophenia. It was (oddly enough) the first of the two I listened to, and it was during a pretty turbulent period of my life (first love and all; what a waste she was). It ain't easy being 14. That was years ago, thank god, but that album helped me get through everything that was going on. I think every teenager should listen to it. Its story is essentially about finding yourself and not getting swept up in what the crowds around you are doing, which will probably be perpetually relevant to the teenage demographic.
Musically, it's an all out masterpiece. Anybody who said at the time this album came out that rock music couldn't be intricate and musically accomplished needed to have their head examined. The layering and repetition of musical motifs, the gamut of emotions conveyed, the seamless narrative throughout, and some of the best playing chops our time (and times to come) will ever know combine to make this album one of the greatest ever made.
Tommy, for all its brilliance, lacks that cohesive quality, that singular vision that sets Quadrophenia apart. Not to mention that the performance of Tommy isn't as competent as that of Quadrophenia, and the production and arrangement on Tommy leave a lot to be desired. The group improved dramatically in the four years between those albums.
The album covers, though, are a different matter. Tommy's is one of the most iconic covers ever made. Quadrophenia's was indecipherable to me for years, and even now that I know what's going on it still just registers as a black and white photo in my mind.
By the way, I'm bringing up this mildly dated thread because I saw The Who just last Saturday on the Quadrophenia + More tour. Pete Townshend said they hadn't played the album in full since 1996, which was years before I would have heard it for the first time. It was a brilliant show. They're definitely not in their performing prime anymore, but man have they got energy. They had to do a bit of simplification to the arrangement to do it live, but it worked very well.