I have the AT&T E970 variant (16GB internal, 8MP camera).
The only "....has stopped" error message I keep getting is when using Gmail and only when using the in-app back button to return to message list from within an open e-mail. I've only had my G for two weeks. I immediately updated to JB 4.1.2.
AT&T sales rep said people had issues with the update when it originally came out (month before I got my phone). I had a location data issue after updating (which took no time on this phone) but a factory reset fixed it. So far I've had only minor issues. The Gmail thing is annoying but I can use the capactive back button at the bottom of the display as a work around. In all other respects, the Gmail apps is slick and stable.
As for your SMS issue; I immediately went to Handcent. I'm a big dork and like to use Emojis which the stock SMS app does not support. Handcent is excellent and I have had no issues with it. Did you do a factory reset after updating to JB? Oh and if it has not already been suggested, use the paid version of Helium (formerly Carbon) to completely back up your phone's data and configuration before doing a factory reset. As fast as this phone is on downloads and installs, re-installing 216 apps was not fun.
I have been texting like a fiend since I got this phone (I am up to 1,616 in this billing cycle). My SMS never crashes or force closes. I'm wondering if my specific device was part of a later batch of devices less prone to the issues posted here. The only other thing I've done is disabled as much of the crapware from AT&T as I could to free up RAM. I am hoping for some stability patches from LG/Google just the same.