I am going to kind of go along with what some of the others have said. They are all good phones.
I have used BB, Android, and am now I am using W8. Wife used iOS for 5 years and now she is on W8 too.
I say that to say, it really matters more as to what you want in a phone, how you will use it, and if there is a specific type of OS you enjoy the feel of.
Probably what matters as much as anything right now, what carrier are/will you (be) with?
To mirror some of what was said in earlier posts, best thing you can do is go to the store and try them out.
-GS3 is an awesome phone, many people have them, and it is solid all around. From the people I know that has one, everyone says the battery life is on the low side, but they love the phone.
-The Lumia 920 is wonderful. Battery life is pretty good so far, wife says it is better than her iPhone 4 was. Great pictures (update coming to make well lit better) OS is butter smooth, just not the customization options of Android. The interface is really nice though.
-The iPhone 5 is a very solid and is very good at what it does. I describe it as a phone that tells you how you are going to use it. If you want to use it as it is, then iPhone is your choice.
-Nexus 4 is very solid, will have support for a long while, as the others listed will too. The storage limitations bother me personally, but may be fine for you. LTE would be nice, but if you are in an area that doesn't have it, then it doesn't matter.
Ultimately....I would say, find out what is important to you. Battery life, interface, camera quality, app variety, what? Use that to put the phones in order based on what you decide you want, then go check them out in the store. Tell them to leave you alone for a bit and play with every option, then ask questions.
Hopefully that will make you most comfortable with the decision you make.
Enjoy your phone, whatever it may be. They are all solid choices!!