A bit of reassurance first up - they're both great phones.
However, you do need to choose, so here are are three criteria that may be helpful.
- Have you got a preference for size?
The Samsung Galaxy SIII is a big phone. Not chunky, but it has a large screen - 4.8 inches on the diagonal. The iPhone 5 is the same width as the previous iPhones, but the new model has a taller screen - bringing to 4 inches on the diagonal (older iPhones has a 3.5 inch screen).
Now some people really like having the big SIII screen. They prefer it for watching videos, iPlayer, reading books, internet etc. Other people find the screes too big - the SIII feels too unwieldily in their hand.
It might be worth getting hold of a SIII just to check how comfortable you are with its size. Depending where you fall on that criteria, you might have your answer there and then.
- Are you an Apple household?
By that I mean do you have other Apple devices like an iPad or Macbook laptop? Do other family members use iPhones? Did you previously have an iPhone? If so, there are advantages in staying with Apple. Firstly any apps you bought for a previous iPhone can be used on your new iPhone 5. You can also use apps you buy in the future on your iPad if you have one. Apple also has a feature called iCloud, which can sync your music, documents and photos between devices - for example if you take a photo on your iPhone it pops up automatically on your iPad or Macbook. So if there is already Apple stuff in your house, there could be synergies in staying with Apple for your phone. One downside to be aware of with the iPhone 5 though is that the charging cable on the 5 has a different socket to the one used with iPads, iPods and the iPhones before the 5. You'll get the new charging cable with the 5 - but if you're used to having several Apple chargers around home and work, you'll need to be prepared to carry your charger with you, or buy a spare.
Naturally if you have no other Apple devices in your house, and don't already own a bunch of iPhone apps, there is no switching cost involved in going with the Samsung Galaxy SIII.
- Are you on a budget or in a hurry?
The Samsung Galaxy SIII is widely available for free upfront on a 2 year contract for around £36 / mth. The iPhone 5 will cost you around £100 upfront on the same types of tariff. Are you happy to pay the additional £100 or are you looking to save money?
Finally the Samsung Galaxy SIII is widely available at all outlets. The iPhone 5 is in short supply, and most outlets require customers to order one in - this usually takes 1-2 weeks. If you can't wait for a new phone, you may struggle to get hold of an iPhone 5.
I hope that helps. I'm happy to give a steer on network or tariff if you get stuck. Good luck!