Yeah, if you're not playing in 720p or 1080p on a modern handheld or modern TV, the quality will dip. In my opinion, the best way to play it is using the most up to date version of Mesen or FCeux and in 1080p on a 4:3 monitor.
I'm lucky I have a NT Mini Noir. I can adjust so much video/color crap and change to any color palette on the fly. I have been spoiled. I don't even own an actual original NES. I do have a crappy $20 Hyperkin, and it does looks really good on it. It is indeed a very strange thing that my game looks good on everything but an actual NES, lol. Go figure...