Aside from the visuals (4:3 to 16:9, etc), converting the analog console signals into digital formats for your flatscreen creates lag, enough to often ruin the gameplay.
I played some Mario Bros 3 and... I kept dying. Jumping too late led to running into holes and enemies. It was so bizarre, I couldn't believe how bad I'd gotten. Tried the next day, same deal.
Then I had a thought re delays. Pulled out my NES and hooked it up to the CRT and all that stopped
There was sufficient delay in the NES mini and modern TV it made a huge difference.
I'm sure I could retrain myself, but it was honestly stunned at how much of a difference it made
That said, if you ever get an urge to play Mario on modern hardware, try run ahead emulation. It’s quite magical.