Some factors that I can think of are:
1. Cost - FSI is usually more expensive.
2. Location of facility offering your aircraft - reduces travel costs.
3. Availability of training slots - if you are in a hurry, this matters.
4. Quality of training.
5. Loyalty to one company because of experience with them.
6. Price as determined by your years with brand X, i.e. everything is negotiable.
7. Weather anticipated - hate Wichita in the summer!
