The biggest difference between shipped, cooled semen, AI and live cover is efficacy. I rarely have to re-breed a mare I live cover with my stallion. Mind you, I only live cover my own mares, so any risk of injury to mare or stallion is all on me. If someone sent me a mare to cover, I would actually collect the stallion and then inseminate the mare with the fresh collected semen.
I don't know about other breeds but Arabian stallions in high demand tend to extend the semen too much, IMO. Rarely do I hear of a mare catching and settling on the first insemination. That can add up pretty quickly.
Cost comparison to do live cover vs shipped & AI:
Stud fee: $1500, no matter whether live or AI
Collection, handling and shipping: $500 (so if you need 3 shipments, $1500)
Shipping container deposit: $250
Vet costs to palpate, ultra sound, inseminate, and routine drugs: $400 PER CYCLE, (so multiply that times however many times you have to try before she is pregnant)
That's just the basic charges.
Mare care $8/day dry and $10/day wet, or $250/mo & 300/mo if the mare stays more than just a few days
Chute fee or handling fee: $200 (no matter how many times I collect the stallion and inseminate the mare)
Insemination materials: $100 per cycle
There can be a few extra charges for live cover, for instance if you ship me the mare in the end of Feb in preparation for breeding in March, I'll add a teasing fee of $100 for the entire stay.
With either, you will have to haul the mare to the stallion for a certain amount, or you'll haul to the vet. Or, if the vet will come out and do it at your place (if you don't have good solid breeding stocks, they might not), you're looking at a trip fee or farm call on top of the cost to do the insemination.
Some vets don't do an all inclusive rate like mine does. You can be looking at $60 per ultrasound, $30 per palpation, $200 per insemination, $20-40 per injection if they routinely use hormones or oxytocin when AI-ing the mare. Mine charges around $400 and it includes EVERYTHING for routine exam and insemination. There would be extra charges if they discovered the mare was dirty, for instance. I always culture my mares prior to breeding, so I don't get any surprises there.
For me, I've found I prefer to use live cover. So, drop off the mare for about 1 week to 10 days, if she's showing heat the day you drop her off. Go back and pick her up when she goes out of heat, have the vet check her at 17-20 days from the last time she was bred and see if she took. A LOT less hassle.