Alyse,
You might want to read
Andrea Pecor's Personal Profile. She's one of a number of AA patients who have had ATG more than once. Some patients who received horse ATG switched to rabbit ATG, or vice versa, looking for more benefit, while some used the same type because it worked before.
When Andrea had her ATG there weren't any other treatment options. It may be hard for you and your doctors to decide between treatment choices but it's actually a benefit to have a choice.