So, I foolishly upgraded my 3GS to 4.3.3 (from 4.3.2) yesterday. I immediately experienced the same problems mentioned here, cellular service in general is virtually unusable, and battery life *****.
I'm still experimenting with the various battery-extension suggestions, but I can definitely confirm that disabling 3G solves the cell signal strength problem.
I just did a test, while standing in town bathed in the glow from my cell tower lights. With 3G off, I got full bars. When I turned 3G back on, the signal dropped to zero within seconds, and bounced between 1-2 bars and "No Service" (mostly the latter). Turned 3G back off, full bars moments later. I did *not* have this problem with 4.3.2, so this is a definite bug in the latest software, and I strongly recommend everybody avoid it (well, if you like to make phone calls or anything like that).
Note that 2G (regular cellular data) can be left on. So you get *some* data service, just not the fast stuff.
This is an older phone, so it's possible there's some other factor that exaserbates this. I'm not entirely certain how to collect whatever data may help narrow this down, but I'm willing to offer any troubleshooting tests.
Brad.