It would be interesting to break this survey down into two groups: one that left their N3 alone and use it pretty much stock from the carrier, and the other that rooted it, and fiddled with the TW and carrier software a bit.
Rooted, Safestrap, currently testing X-Note. (Wish it was a 64GB device so I could have a few more slots.)
I can't think of another phone that actually exists that I'd rather have. I can think of features I'd like to have, but I'd like my car to be able to fly over traffic jams too.
This is the 3rd Note 3. OTA bricked the first one. Storage went on the second one. This one works, update is frozen (at least until 4.4's been out and stable for a while, there's a way to root it, and there's a Safestrap for it).
It's a bit large for a shirt pocket, and dangerous for a pants pocket (I bend, it doesn't), but with my cataracts (soon to be corrected, I both dread and hope), I need the large screen.
Coverage is great where I am, wifi and BT work, there's just no way to get it to wirelessly mirror to a Vizio TV without adding something.
So - one muchly modified N3 and I love it. Oh, Nova launcher. Hate TW, always have.