both can be had for about same price. A small advantage for compu stick is that its windows and thus easy to get things working.
But which would be more powerful to emulate up to PS1/N64?
I'm prety sure that the compute stick is about twice as fast as the Pi 3 (based on Dhrystone and Sun Spider scores).
With that being said, both probably serve your purpose. I personally prefer the compute stick because I am more familiar with Windows, but the Pi 3 appeals to the tinkerer in all of us.