It's interesting to see everybody's response and how it's based on their current lifestyle and what you'd have to do to maintain it given a certain sense was taken away.
I said that I'd rather be deaf than blind. This is mainly because of all of the things in my life that would need to change if I were not able to see: being able to practice the area of medicine I want rather than switching to something I can do without vision, drive, play tennis, lacrosse, ski, free running, video game, etc... pretty much everything I do for career or hobby.
Could I do all that without being able to hear, certainly! It's not like any of those things I listed above require the ability to hear. Reading lips and having simple conversations is quite easy in most settings. I'm pretty sure I could make due in pretty much every sport I play as a hobby without being able to hear. Nodding and hand signals are basically enough and then with a bit of lip reading and my ability to speak to my teammates or opponents fluently ... not sure what the big deal would be, but good luck returning a serve if you're blind.
A career in medicine is certainly possible without hearing, I imagine much easier than if you're blind. There are charts, prelim interviews/histories by nurses, lip reading, body language, computer screens, etc... this is all without mentioning the quickly growing technology of voice to text human-computer interaction.
The people who said they would rather lose their sight obviously engage in activities where their vision isn't that important, or at least they would have to undergo a bigger change in lifestyle if they were to lose their hearing vs lose their sight.
I had an extra credit assignment in a psych 101 class back when I was in college where we had to spend a day blind (complete eye/head coverings) and spend a day deaf (ear plugs + noise reducing headphones over the ear plugs).
I was much worse off without sight but my day was completely normal with the ear plugs and headphones, minus being able to talk on the phone ... it was basically just quieter, and a cashier had to ask me if I wanted a receipt two times since it took me a few seconds to read her lips and get the little hand gesture she made. I played tennis with no trouble at all in the afternoon, other than having clunky earphones on my head. My friend and I had to write a bit to each other when we ate dinner together, but even then we were able to talk kinda normally until we changed subjects. Later that night, I composed a brass quintet piece for homework in my theory/composition class with no trouble not being able to hear.
My blind experience was a bit more limiting to my youthful lifestyle. I had a lot of trouble going anywhere without assistance from my roommate. I couldn't play sports with friends. Most of the routine stuff in your house (or my case, dorm room) was fine since you know where stuff is. It just takes a lot longer to get it done since you're new to having to feel around for everything and not running into everything. Conversations with friends at dinner were still the same, the only time I missed out was when a friend showed a picture they took the night before. Even though I had to skip on a sporting activity earlier in the day, I was still able to work out in the university gym without trouble, just minor assistance from my normal workout partner ... he was still comfortable with me spotting him.
The purpose of the assignment was to realize how much we rely on either of our main, non-tactile senses to gather information and interact with our environment. It also gave us a bit more insight into the lifestyle of those without those senses and helped to understand what all you were still capable of, especially after you adapt and how much you can still experience, like losing a sense or even several isn't a death sentence, it's just a different way to interact with your environment that you need to adapt to.