You can breed rats or mice in your garage depending on the temperatures- they don't breed very well when it's colder, & they're going to die when it's summer
unless you modify your garage. When I lived in the desert, I raised lots of rodents in my huge garage: I had a down-draft 'swamp-cooler' installed on my garage,
and it was controlled by thermostat. What worked really well for me was having 4 up-ducts installed in the ceiling (it was a 4 car+ finished garage) so that the
warm (& smelly!) air went up up & away while the cool air came in. Very cheap to run, even in a huge garage. You'd probably spend more on electricity using
an A/C in a shed, & a garage that's attached is likely more insulated than a shed also. I didn't need to heat in winter, just added deeper bedding. Really depends
on your climate though. If it's too humid where you are for a swamp cooler to be effective, then the smaller shed might be best. Just keep in mind that you can
lose your investment much faster should the power fail...in a large garage, you have more time for the temperatures to change.