Depends on what you have in the guts of your cabinet. Most cabinets are really a very ornate tower containing a very simple, singular motherboard to operate one thing; whatever game you have. I'd assume any emulator you put in a cabinet would be on a far more elegant (and generally speaking, more power consuming) motherboard and an actual drive to hold the emulator program as opposed to a ROM file built into the board. However, with emulation you can actually record save data, such as high scores, and power down most machines, whereas with an actual cabinet the scores reset on powering off. The drawback to emulation is it's fuzzy legality.
In short, it'd use about as much power as your PC depending on how long it was on.
"Laugh and the world laughs with you. Frown and the world laughs at you." -Me.
I actually have a spare Scope and copy of the game. I bid for them on Ebay for the same max price and ended up getting the sencond one about half what I got the first one for. I'd be happy to let you by it off me!