Mostly answer would be : it depends.
Effects framework gives a big advantage that you can set your whole pipeline in one go using Pass->Apply, which can make things really easy, but can lead to pretty slow code if not used properly, which is probably why microsoft decided to deprecate it, but you can do as bad or even worse using multiple shaders, directxtk being a pretty good example of that actually (it's ok only for phone development).
In most cases effect framework will incur a few extra api calls that you could avoid using separate shaders (which i agree if you're draw call bound can be significant, but then you should look at optimizing that part with culling/instancing techniques). Using separate shaders you have to handle all state/constant buffer management yourself, and probably do it in a more efficient way if you know what you are doing.
What I really like about fx framework is the very nice reflection, and the use of semantics, which at a design stage can be really useful (for example, if you do float4x4 tP : PROJECTION, your engine can automatically bind camera projection to the shader).
Also layout validation at compile time between shader stages is really handy for authoring (fx framework).
One big advantage of separate shaders is you can easily swap only the stages you need, so you can save a decent amount of permutations, without touching the rest of the pipeline.