I too updated last night to 6.1 (tried the 6.02 update as well and that didn't fix my problem). I called the Hertz # today and it sounds great, no choppy cut-outs even with only one bar of volume (lowest setting). Before the upgrade I had to listen with the volume set to at least 5 bars to avoid cut-outs.
I think Apple may have finally fixed this. I'll claim victory when back home in my local cell footprint where I make most of my calls from. I know the Hertz-800 # issue was exhibited there. Oh, and this is a Verizon phone.
Again, for me, the main issue was choppy cut-in and cut-outs when the other party was talking low (like folks around a speaker phone in a conference room and someone a ways from the mic) and when I am using the headphones and I have the volume low on my end, like 4 or lower. Having others on the other end talk louder and turning up the volume on my end, until today, seemed like the only remedy to avoid the choppiness.
I *REALLY* think this is (was) a "low source volume + low output volume + over-zealous noise cancellation" *BUG* (patent pending on the bug title)...and I am hoping it is fixed.
Will claim it fixed when I do more testing, but for now, MUCH BETTER!