Did you read our reviews:
http://reviews.cnet.com/smartphones/htc-droid-dna-verizon/4505-6452_7-35536642.html
http://reviews.cnet.com/samsung-galaxy-s3-review/
I'm sure you'll be able to find many more reviews with Googe. Then see what you find the most important features you want to have in your phone and compare these two models on those features specifically.We can't do that for you.
Kees
IF ANYONE COULD HELP THAT WOULD BE GREAT. I AM SWITCHING TO VERIZON AND WOULD LIKE SOME HELP DECIDING BETWEEN THE DROID DNA (HTC) OR THE GALAXY S3 (SAMSUNG)????

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