You could do both!
I mean the cabinet has some controls already. Maybe leave it like that, stick in a PC and add your console emulators.
Then all you would need is a simple USB controller card for maybe $20 to plug your existing cabinet controls into. Install MAME. That's it! Now you have a working arcade machine too, if you're interested in that.
My standup cabinet plays mainly MAME, but also some driving games ...Daytona, Sega Rally, and some newer PC racers too.
To play the racers, I have an HDMI and a USB extension running to my 60 inch plasma in the other room. I have a nice low chair with a racing wheel (it's a massage chair too haha).
So I use the computer in the arcade cabinet to play racing games in the other room as well. Works awesome. I have a wireless keyboard and mouse near the steering wheel. I can use the computer as a computer from the big screen also, as an added bonus.
Also, I use the same computer - for now - to test my cocktail cabinet. Just run a few wires....
Anyways, point is you can do a lot with that cabinet. And if you get tired of standing up playing console games you could maybe do what I did and play from another TV.