I have had a variety of phones from 5.2 - 6.4" screen size.
Storage:
Back jeans pocket or in a purse. If in the back pocket, then I take it out before sitting as to avoid bending and repeated stress.
Occasionally a jacket pocket but the additional weight (a few more oz than 5") can make coats sag or hang off center.
Sizing:
Once a phone crosses into two hand territory, then I pick the larger size ( One handed use is towards 5" for me)
Large phablets can't be too wide for one handed grip. I tend to sit while using kindle/tablet/laptop but standing or moving while using a smartphone (nav, calendar, etc),
6+" acceptable for me as a replacement for 7/8" tablet. 7/8" tablet are too wide for one handed grip. Anything larger than that, I'll want at least 10" and a good keyboard oriented towards productive output rather than consuming input.
Usage:
Phone calls don't make up the majority of my smart device usage time and when I do need to make a long call, my headphones have a mic which improves audio (ear and speaker) quality. A large phablet next to my head does look quite funny. Thankfully people are now used to assuming that speaking off into the air means bluetooth and not talking to yourself.
Larger screens let me process email more quickly
I'm also still waiting for the waytools keyboard (two years and counting!) which would be quite useful for extensive typing, yet still fit in a coat pocket or purse.