When to use a roux or a beurre manié
There's a great overview of the differences here, including a taste-test experiment at the end. 

Broadly: beurre manié started off as a "lazy" roux; some people claim that the cooking of the roux reduces any "floury" taste; the experiment did not find any discernible difference between the two options for either a bechamel sauce or a velouté.