Welcome to the forum, Leighton.
I for one cannot give the simple reply that you seem to be seeking. Why not? ... because (in my opinion) the success of MES depends very much on the circumstances prevailing at the original setting.
For example, if (just imagine) the in-house biomed department is utterly useless, or desperately lack resources of some kind, then it is very likely that the MES contractor will shine!
Also, the MES company may be contracted to provide a skill set not available in-house (maintaining some special kit, or whatever).
MES also works well as a method of consolidating into one all the hitherto many and various service contracts with outside service providers. Is that likely to be cost-effective? Yes, I would say so. It also makes things so much easier for the in-house manager, as well (that is, there is only the one number to ring)!
If the MES contract is well set up at the onset (that is, by a client who knows what he wants, and what he is doing), and then properly managed (monitored, measured) during its implementation and operation, then there should be no reason why it should not be a great success. Not (necessarily) to replace the in-house department, but to
enhance it.
However, if the whole thing gets badly sold to the in-house guys, and ends up as an "us and them" p***ing contest ... well, that's not much help to anybody. It's always easy for hospital folk to "close ranks against intruders", if (for some reason) that is the prevailing mind-set. And I know, 'coz I've been there!
But at its best, the MES Model is good for rounding the circle, covering the bases, crossing the T's ... and getting the boxes ticked!