I ended up setting up shop in my basement. Stays fairly cool in the summer and is reasonably warm in the winter (although I plan to add a space heater to make winters a bit more comfortable).
In your case, I'd probably opt for the out-building, especially if your wife plans to continue using the garage as a garage. You will find that there is never enough room in your workshop, and I would guess that the outbuilding will give you more flexibility to expand set up benches, storage, tools, etc. to your liking. Of course, I guess this would also depend on how long a trench you need to dig to get power.
Wherever you set up, be sure to invest in plenty of electrical outlets and plenty of lighting. And a flat, stable building surface is a must.