In years past, our Stake had issues loaning out equipment to another stake (came back broken and no one accepted responsibility).
Our policy now is: If there is an urgent need (definitely if there is an emergency), by permission of a member of the Stake Presidency or Stake Clerk, the equipment is to be accompanied by our STS, our STS is responsible for any damage and/or replacement.
I have assisted 5 other stakes on as many occasions loaning some of our expensive equipment to them, and I accompanied the equipment, helped them set up and made sure everything was returned in good condition. In five years, we have had only one mishap, a flat screen monitor was dropped, broken and needed to be replaced. Fortunately the cost of the replacement (used) monitor was only $50.
On the other hand, when we needed to borrow equipment from one of the other stakes, they were very willing and accommodating to us.
IMO, it is not practical to share the same equipment since both Stake's Conferences could be on the same day, but cultivating a relationship with neighboring stakes has been beneficial for both our stakes, especially when one needed to borrow something.