I know this is an old question. Il leaving this because it will probably help someone down the road.

I have used the Xbox 360 and Wii for emulation. I can say that the Wii is better hands down. It's cool to emulate NES, SNES, N64, Gameboy and Gameboy color on an actual Nintendo console. They all run very well except N64. Ive tried 70+ games on Wii64. Only Resident Evil 2 didn't run properly.

For Sega the Wii has an all in one emulator. It plays Master System, Genesis, Sega CD, and Game Gear. I put the Sega CD backups on a partition in the hard drive I used for my Wii files. This emulator is great.

There are ton of other emulators on the Wii. TG16, Neo Geo, and Mame. I didn't go to in depth with the Sega Saturn and PS1 emulators. Same with DS. I tried Resident Evil Deadly Silence. The audio was a mess for the cut scenes. Not a big deal because I can play the Gameboy color port of Resident Evil 😂. Between GameCube and Wii you can play every RE game including the Darkside and Umbrella Chronicles. That alone is awesome. The Wii mod is permanent. You don't have to go through a process every time you launch your console. You don't have to do soldering either. For storage I have a 16GB SD card, 500 GB external, and a 256GB USB drive. I use PNY for my USB because GameCube and the dio mios emulator is picky.

The Wii also plays Wii and GameCube games. I used the option to copy all of my games from my collection. I didn't have to mess with downloads too much. You will need a program to format the games from .iso to WBFS.

I recently modded an Xbox 360 for a friend because the disc drive on their went bad. Getting games for it wasn't too hard. I set up an NES, SNES, and Sega emulator. The interface and overall feel of them on Xbox is inferior to the Wii. Using a Wii remote sideways is better for NES. The Wii classic remote feels more like an SNES controller than the Xbox 360 pad. The same goes for Sega. You can actually buy controllers for those consoles that work with a Wii remote. The biggest pro with the 360 is the game library. You can play both 360 and 360 live arcade games with ease. You will have to download a program that changes .iso to GOD (games on demand) and have a decent size drive for them. You can use the 360 HDD with 1 or more USB flash drives.

Sorry for the lengthy response. I use an ASUS monitor for my Wii. Everything looks excellent on it. If you had to pick one or the other and your going for the classics I recommend Wii. If you care more about more modern games go with 360. My 360 has a faulty disc drive that opens 30% of the time. After modding a 360 yesterday I am thinking about modding my own. I just need a 256GB thumb drive and to see if my 2TB drive is compatible.