Governments answer to the voters--in theory, to almost everyone. Corporations answer to their investors--many of whom don't even live in the area the corporations operate in. In government projects, corruption is sometimes a problem; in private projects, some things that would be illegal corruption in government projects are legal, like hiring the CEO's brother or hiring a more expensive contractor who you think will do a better job. Private companies have to make a profit. Public agencies face political pressure to treat employees well, which can raise costs. Private companies with shortish-term contracts have little incentive to plan for the far future; government agencies might, if constituents pressure them to.
It matters how the contracts are written. It matters how the subsidies are arranged. It matters how oversight is done.
I don't know if it actually matters whether the T or a contractor operates the CR service.
I think it does matter how well the CR is coordinated with rapid transit, T buses, RTA buses, Amtrak, and whatever other services might exist. The Needham Line and the Fairmount line kind of fill gaps in the rapid-transit network. Reading trains and Lynn trains serve stops that in some plans would have become rapid-transit stops. CR is kind of an express service for the orange line and for the Braintree line of the Red Line, although few people use it for trips that short and we wouldn't want the trains to fill up with short-trip riders instead of zone 5 people. Lots of CR riders change to the subway for their last mile on the way in; some use buses to get to the CR station and more could if there were better bus service to CR stations in places like Lowell, Worcester, etc. Whoever runs the systems, they should work together better than they do now.