I switched carriers and got the Note 4 because of the $200 preorder promo. My 64 year old eyes don't see any difference with the screen, so I bought another Note 3 and am plenty happy to stay with it until the Note 5 or better comes out.
Just shows you have subjective comments and opinions can be, and they all be correct.
I am 74 years old, and I went from the Note 3 to the Note 4, and screen is one of the differences I do see. Sure, the Note 3 screen is so sharp it cuts you, but the Note 4 screen is so sharp it not only cuts you, it makes you bleed real blood.
I will admit, the jump from the Note 3 to the Note 4 is not gigantic, for the simple reason, the Note 3 is still going strong. Hard to improve on an almost perfect phone. The Note 4 added some increases, not much, but they are there. I am a happy camper and as soon as Samsung mentions a Note 5, I want it!