The downside of ANY contract management company, whether it be Aramark, Crothal, HHC, Johnson Controls, Morrison, or Sodexo is that you need to meet the demands of both the client and your company. Sometimes that takes a contortionist's ability.
Client's can decide to give the contract management company the boot and then you will be left looking for a job. Most contracts have 60-day or 90-day out clauses. A client can change for example, the person at the hospital to whom you report, or a CEO of a hospital may change. That person may like another contract management company and decide to give you notice... or they may not like contract management companies and decide to take it "in-house" or "Self-Op" and you typically sign a Non-compete clause when you join Sodexo (or any other contract Management Company) especially at the GM level. In that case, you are out of a job - even though you may have been meeting all the performance requirements.
One other downside is that there is an internal group whose purpose is QA, called "Brand Management" that is a good thing, really, but some of the members of that group can be petty. They need to justify their jobs, so they come around and point out flaws without consideration of how to fix things for those on the operations side of the business.
I have had a great District Manager and Smart Senior Vice President, but that is not always the case, and if you are unlucky, you may endup with someone who just wants you to cut corners to improve the bottom line.... this is true of every contract management company.
Sodexo's background is Food/Nutrition Service, often they don't understand the challenges of the GM's in non-food operations/accounts.