I'm looking at a horse trailer with a permanent rear tack versus the collapsible one. I've never had one before so I wondered what the pros and cons were. Which is better - permanent or collapsible? Why?

I personally dont like a rear tack at all. I think I'm the minority, though. I like a big wide opening for loading and unloading instead.

I like not having shavings and crap in my tack room.  I never actually collapsed my collapsible unless I was pulled mats and had to.  The one I had you still had an upright support between the rear doors, so it did not open up the 100%.  I do know folks who have a removable support and have hauled 4wheelers and such to camp grounds in their horse trailers.

We have a stock trailer if we need to have a wider loading space.

This. I prefer a permanent rear tack.  

I custom ordered my trailer to have a permanent rear tack.  I did not want shavings, urine, etc. going in there from the horse compartment.  Mine is completely sealed.