The Razr Maxx is the perfect phone for me. The majority of the time spent on my phone is for calls, texts, e-mails, calendars, to-do lists, and using it as a mobile hotspot. Having the phone last while tethering was definitely something important for me because if I want to watch movies or play games, I just tether the internet to my laptop or Nexus 7. I use my phone for basic phone needs, really, and have my other devices for a better visual experience.
In terms of signal, Motorola radio's are pretty beasty and I haven't had any issues with calls or data. I live around a lot of 4G LTE so I'm pretty much covered in that aspect.
With ICS, the UI is very responsive. I haven't had much, if any, lag going from screen to screen or app to app. I honestly haven't had any complaints about the display either. It looks good to me and I don't have any real problems with it.
The one thing that's lacking for me is the camera. The images aren't that great, but videos aren't too bad. There have definitely been better cameras, but again, I mostly use my phone as a phone.
Having a constant 4G LTE connection and being able to tether it to my other devices for up to three to four hours and still have enough charge for the rest of the day is something pretty special to me. You could of course get a better or external battery for the SGS3, but out of the box, the Maxx's battery is non-comparable.
This has been my experience with the Maxx. I've only had the phone for a little over a month and had the option to pre-order the SGS3, but went with the Maxx and have not regretted it one bit.