There would be no question if it were me getting a new phone. I have had the Motorola Droid and Droid X, then I moved to the Samsung Galaxy Nexus (first Samsung device for me) and this is the first and last Samsung I will ever own. I absolutely hate this phone. The battery life is horrible...I finally had to purchase the Seidio 3800 mAh battery to be able to have any kind of battery life.
Then the biggest problem of all with Samsung phones is the crappy/horrible reception. This Nexus constantly is either dropping calls or my phone never even rings and just simply goes straight to voice mail. So, Samsung will never be an option for me...ever! Go with the Razr Maxx HD...Motorola makes the best radios.
Clearly, you didn't live through the "will we or won't we?" upgrade saga for Moto Droid Bionic users (ICS debacle).
I switched from S3 to Maxx HD *only* because Verizon didn't unlock the GSM feature of S3. I already purchased the 3500mA battery for the S3 so the length of use was the same (of course, no doubt Maxx HD looks much better!).
S3 camera is EXTREMELY quick. You can take multiple shots like a decent DSLR!.
S3 does not have "Favorites or Smart Actions" So that's a nod to Motorola.
S3 has more functionality for home screen setup. I'm not sure why Moto default to home page being the first page after the shortcuts page. I wish I could make my median page to the my home page.
S3 allows different backgrounds for lock and home screen. Moto doesn't.
Looks...again, it's "to each his own..." but clearly the MAXX HD (to me) looks better. not as "plasticy" Some might say that MAXX HD is very much like I5 in looks.
S3 has its own Swype, but Swype (beta version) is better. Moto comes with full Swype.
Moto doesn't allow you to add the google search bar to only *one* home page. I have no idea why they did that. S3, it's up you.
HW wise, it's about the same.
S3 allows for replaceable batteries. Maxx HD doesn't. But for me, this is a non factor. By the time my battery is about to die (and can't keep a charge) I'm sure I''ll be ready for an upgrade.
Both are good phones, you probably can't go wrong with either one.
(But keep in mind, stock HD vs stock S3...battery life is not even a fair fight!!)