If you are debating between the two phones, only your opinions, needs and wants matter. I'm assuming that you are comparing an iPhone 5 and a Samsung Galaxy S III. The overall functions of the phones are similar. For the things that are different, the better phone for you will depend on your preferences entirely.
I'm not a fan of iPhones, but I recommend them to other people based on other things in their lives. I love the Galaxy Note II, but wouldn't recommend it to many people that I know. The Galaxy S III is a decent phone but depending on how one plans to use it, I may or may not recommend it.
When people ask me for recommendations, I come back with a bunch of questions. Some people like these questions, but some don't. Some of those questions are below:
1. What phone do you have now? Why do you want a new phone now?
2. How do you plan to use your smartphone?
3. Is there anything that you have noticed that other people do with their smartphones that you would like to do, as well?
4. If you plan to use your smartphone to play music, watch movies, or store and view photos, how do you manage your media now?
5. Are you comfortable having your media content in the cloud, or would you prefer it to be on your device only?
6. Do you use your speakerphone or BT devices when you talk on the phone?
7. What phones do your friends and family have (the ones that you talk/send messages to the most on your phone)?
8. How much are you looking to spend on your new phone?
The answers to these questions usually lead to other questions from me. There are tons of other facets that make one phone better than another one for a user. Either way, there will probably be some level of compromise when you select a new phone. Even though I'm not a fan of iPhones, I can think of at least one thing that it does better than my Android phones for my personal usage patterns. But after I weigh the pros and cons, an Android device works better for me.