Beartooths – Base out of Cooke City or Box Canyon?

I might have a chance to basecamp out near the Box Canyon cabin OR out of a cabin near Cooke City for 7-10 days this summer. Would be looking to put together some day hikes shorter backpacking trips, and/or maybe do a 4-5 night trip.

A) Any pointers on whether to base our of Box Canyon or Cooke City? From the looks of the map, it seems like Box Canyon = much more solitude, but perhaps fewer trail options?

B) Any tips on best time this summer? In olden times, I would have looked at August for less bugs, but now I fear the smoke.

Any/all advice appreciated.