In my experience, generally the renter/farmer holds the hunting rights, unless it's explicitly worded in the lease otherwise. It's their crops really and they are renting the land...

We have actually had problems the other way Land that my family farms/ leases and the owner's giving hunting permission to others (which can get dangerous, especially if they are hunting with firearms). In our case, a simple conversation with the actual owner cleared things up - they now send anyone seeking permission our way...

I suppose it's different in every situation.... As was mentioned, the best thing is to get everyone of the same page...