this is an extremely hard question. (Ignoring those that are saying things about eye transplants for that is an unintended option that the OP wasn't either aware of, or isn't really supposed to count. (Not to mention that there are MANY blind people out there that leads me to believe that eye transplants aren't that easy to come by. (Either insurance doesn't cover it or it's extremely difficult or something. I'm not that educated in that sort of field so I'm going on assumptions here.)
As the rest of you, gaming is my main hobby, and it is a hobby that usually requires both sight and hearing in order to fully enjoy. Now some will say that sight is definitely more important in that field than hearing is, and I fully agree, but my main issue is when it comes to games, is that I play MORE by ear than I do by sight.
I've trained my ears to pick up the lightest of noises when playing online so that way I have an immediate advantage against those who are against me. I even demonstrated this to my nephew yesterday when playing TF2 without a headset, the difference in how I played without and then with was enough for him to drop his jaw, so one can understand why I love my ability to hear more than the average person.
On the other hand, despite playing a lot better by ear, I think it might be a tad impossible (or fully freak'n impossible) to play almost any sort of video/computer game without the ability to see.
I would probably have to go with sight if I want to be able to keep my hobby of playing games, though sacrificing the ability to litter the battlefields with all that stand against me might just be enough for me to put down the controller/take my hands off the keyboard and mouse.
If it wasn't for me being a gamer, I would probably sacrifice hearing. Most things in the apartment and my room at my parents house never stay in the same spot twice, (besides stuff that only gets moved when you're redecorating obviously.) So finding my way around would be near impossible. Not so much in my room because I would just simply set things up in a way that I can find whatever it is I'm looking for. Where as my girlfriend is constantly on the move these days and she simply doesn't have the time to always put something back in one specific area.
Though if the ability to get a transplant is viable, and easy to come by, perhaps with the misunderstanding posed in the OP with the SWAT team coming in when it wasn't really needed, they'd pay for it, I would probably choose sight, but then again that's a laughable chance in itself that they'd make up for it...
I'm sorry I'm over thinking this aren't I? Ummm... Uhh... Hearing! I'll just have to find something else to excel in... Wait! I'm a guitarist and music is important to me... Shit shit... Can I come back?