Along similar lines, I have no issues whatsoever with my Droid 4 regardless of using LTE or WiFi. However, my wife's Droid 4 sometimes comes up with "Webpage not available" errors, so I am going to have to dig into that to figure out what happens, and I may just do a flat out factory reset and go from there since who knows what app may be causing it. It may be easier to do the FR and slowly reinstall apps until the problem resurfaces (IF it resurfaces).
Of course, if somebody else has an idea, that would be great, too. Maybe our problems are kinda-sorta connected?