You're OK with the Verizon Note 2?
It's a phone. You'll replace it in like 1.5-2 years at the most, anyway. A bit of branding wouldn't sway me. If I could get it without the branding at the same price, but compatible with the carrier, sure, but I wouldn't pay more for it.
I live in Canada, though, so none of that matters.
Just updated to 5.1 Lollipop. Didn't really notice anything different.
Because there literally was no difference.