It really depends on the terms of the leases.
I partial leased several horses before doing a free lease as my "trial run" before buying. The partial leases I did were very unrestrictive since no one else was leasing the horses and they weren't used for many lessons, so I could ride whenever I wanted and still only paid a flat rate (1/2 the boarding rate). If I had wanted to hire my own farrier or put them on a special diet I'm sure the barn would have been happy to let me pay for that as well
The free lease I did was also pretty easy. The owner required the horse to have aluminum shoes (even though the farrier and my trainers all agreed there was no real need for them) and she did his worming herself on an 8-week rotation. Everything else was up to me.
You could run across some really restrictive "free" leases that require you to use a specific farrier, feed a specific diet, get permission each time the horse is taken off the property where the horse is normally kept, etc. I think the type of lease is less important than the terms of the specific contract (well, that and your budget!)