In your case I think a lot of your decision involves which carrier you want to use. The Razr Maxx is only available on Verizon, the One X is only on At&t and the Galaxy S3 is available on all major carriers (Not sure about Sprint). Personally, I prefer Verizon because of their coverage and LTE is fantastic. If you don't have LTE in your area, yet, this might change your overall view since Verizon 3G isn't as nice as it really should be.
My personal manufacturer choices start with Motorola, then HTC, then just about everyone else (including Apple) and dead last would be Samsung. This goes back to what I've said in the past about problems with Samsung radios in Verizon phones. Not everyone has had the same issues I've had, so their view on Samsung is going to be different. Overall, I've had the best experience with Motorola hardware. Everything has just been really solid. HTC has also performed wonderfully for me in the past, but their batteries have usually fallen short.
As far as the processors go, either the HTC One X or the Galaxy S3 will be faster, but that is primarily because they came out later. They are using the S4 processor which is faster and more energy efficient than the OMAP in the Razr/Razr Maxx. The good news though, is that Moto is about to announce the Razr HD which will have the same S4 processor. The announcement is about 2 weeks away (September 5th) and the phone will probably be available in October. Not so close if you have to have a new phone right this minute, but not too far off that waiting could kill you if you don't.
The nice thing about the Razr HD is that it will have a nice large HD screen (4.5" or 4.6"), 2530 mAh battery (not as big as the Razr Maxx, but with the new processor it should last all day and then some), 1.5 Ghz dual-core S4 processor and most of the other features that the current phones will have. The one thing that is a pro to some and a con to others is the on-screen keys like the Nexus.
Here is a little info on the Razr HD:
Tutorial videos for Droid Razr HD leaked, doesn