I am working as a consultant.
My good advice to every customer is: dont buy consultant work as time and material. Buying as time and material puts the wrong incentives to everybody:
-Your own people will feel that they still can just use them as normal workers and keep all decisions (and thus responsibility) to themself
-The consultants dont care, since just doing what your own people tell them without thinking is what gets their monthly timesheets signed. If something goes wrong they can even sell more hours, not less
-The consulting company does not care (and rigthly so since that was not what you asked for) and will send you inexperiences junior consultants wherever possible.
-Coding quality has to be reviewd by your own people (or just accepted as it is)
-Your own people are usually vastly inferior at project management in comparison to the average senior consultant - in a non T&M contract the usual situation is that you get the things done in time or you will loose money.