Most are system-on-a-chip implementations with only okay compatibility. Color palettes will be slightly off or sounds will be a slightly wrong pitch, won't support all carts, etc.
Your best bet for playing your games on a modern screen is to get an FPGA based system, a top loader NES modded with HDMI output or simply use a cycle-accurate software emulator on a computer.
I don't understand. We just need to gather the dragon balls and he'll be back in time for dinner.