Pros are that you don't get charged a farm call so might save a bit of money.
1. You may loose your "doctor-client-patient" relationship with your vet. This is the legal relationship that allows your vet to give advice on issues over the phone. Your vet must examine your horse at least yearly in order for this relationship to be considered valid and for most clients it's the yearly vaccination visit that is the only time their horse sees a vet each year unless there is an emergency. But if you have him out for Coggins tests and dental exams/floatings, you would still have your at least yearly exam. (But why not get the vet to give vaccinations then?)
2. Because vaccines are shipped more times, there is more risk that they may have been kept at the wrong temperature and thus be ineffective.
3. You don't have the medical knowledge or access to the most up-to-date recommendations for determining appropriate vaccination programs for your horse.
4. You really might not be saving as much money as you expect by the time you pay for shipping/handling.