I think I remember the 1505 n 1 boards, and if they are the ones I am thinking of, they use a fairly old version of MAME and a bit underpowered.
If you are using MAME on a computer that you can set up, and you have a lot of time to set it all up right, emulated games can be great. There are a lot of games that are really well emulated, and there are quite a few devs submitting fixes and additions on a regular basis.
If you are using older versions of MAME, or the crappy multi boards that use old versions of MAME, you really are not seeing the current state of emulation. If all of the people who claim to be able to tell differences between an emulated game and the original would submit bug reports, the emulation would be even better.
On a 1505 in 1, there will probably be hundreds of games that don't play right, certainly hundreds that will not be playable with the correct controls. That being said, there will be plenty of games to play. The numbers sound impressive, but even if every game played 100% accurately, there are still not 1505 arcade games that people would want to play. There just weren't that many great games made.
You will want to stick with a multi board though. If he is asking you to look into it, instead of researching for himself, he will not want to spend the time to set up and maintain a MAME setup. It is not even close to plug and play.