Retropie will let you install a slew of emulators, including multiple variations of Mame.
One is based on a rather old version of Mame (v.39). Another is based on Mame v.78. And still another is based on Mame v.139. There are even a few others in there as well. But as mentioned previously, the version of the ROM has to match the versions of Mame.
Obviously the later versions support more/newer games.
So the first decision is what games do you play? Mostly 80's "golden age" games? The RPI3 can even handle some 90's games with polygon shading/texturing reasonably well.
If you want to play Wii/PS3 games, yeah, the RPI3 won't cut it.
As I'm finding, some of the Mame ports for RPI are not as full featured as the PC versions and may not support the control types you want to use. So take that into consideration as well.
If you want to hook up a tiny computer to your TV, and use a cheap wireless XBOX or PS3 controller to play classic games from your sofa, the RPI3 + Retropie is an awesome solution. If you want to build a nice mini or bartop cab with a simple 8way joy and a few buttons, the RPI is great.
If you want a full cab with 2-4 player control panel and a large variety of different control types to allow playing a huge range of games, the RPi probably isn't the best choice.
Having said all that, the cost of entry for an RPi setup is so low you can try it and then decide if you need more.
On the whole, I found getting the RPI3 loaded with software, Retropie installed, ROMs loaded in the appropriate folders, and a PS3 controller working really quick and easy.