I have this problem also. Just had my iphone 5 swapped out for a new one because the reception was terrible. The reception on this new one was great, I noticed right away I had 4 bars, where before I had 2 — until i did the software update (to 6.0.1) — then the reception problem returned, and the bars went back down to 2.
I, like many of you, have the same experience toggling LTE on and off. Off = 3 bars; On = 2 bars. The network reception will read differently sometimes just by leaning a bit one way or the other. My wife's 4S doesn't do this. When I test hers and mine at the same time, side by side, hers comes up stronger. I did a field test with mine and the results are consistently bad. The customer service person at the genius bar said it could be software, hardware, or sim card. So starting from scratch, without restoring, just with the barebones + the update, it's happening.
When I toggle the LTE off and do a field test, my result is -85 (good); When I toggle LTE back on and do a test my result is -110 (bad).
I also notice that when I toggle LTE off for a minute or two, when I first toggle it back on, reception surges to 5 bars for an instant, then goes down to 2 or 1 bars.
I'm in Vancouver BC on Virgin (i.e., Bell network).