It's difficult to suggest any phone as a specific "better device". Unfortunately, we're at the mercy of phone-specific hardware builds, software (updates or just not playing nicely with the phone), network stability (or lack thereof) in your area, user error, etc.
I am really enjoying my GNex and what I've been able to do with it through rooting, but that's user-specific, not something every user can or wants to do.
Maybe a different phone will be your best choice, but before making your final decision, take a stroll through the other forums here on AC and see what likes/dislikes they have posted. I think you'll find that, just like the GNex, there are pros & cons to all of them for various reasons. Below is just a sampling:
http://forums.androidcentral.com/htc-evo-4g-lte/179458-7-days-evo-lte-going-back.html
http://forums.androidcentral.com/droid-razr-maxx/172845-maxx-data-drops.html
http://forums.androidcentral.com/htc-one-s/179573-did-software-update-provide-sufficient-fix.html
As far as the GSIII, who knows? It's a crapshoot with any phone, but since it hasn't been released yet here in the US, there isn't much feedback to draw from except from people who have gotten the international version.
It's a matter of personal choice; no phone is perfect, at least none that I've owned.
But this I do know, whatever your choice of phones, IMHO AC is the best when it comes to mods, advisors, and friendliness of users willing to help other users, no matter what your level of expertise may be.
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