Does scalp hair grow faster than beard hair?

Beard hair and scalp hair grow at a rate where you shouldn't notice a huge difference after a beard transplant. They do have different growth cycles and different hair characteristics so that may not perfectly match.

Everyone is different, but for most people the growth cycle for scalp is longer than beard and therefore leads to longer hair (See Growth Cycle and Anagen).

I think that scalp hair grows faster usually at a rate of 1/2 inch per months. Beard hair grows slower than that although it is probably a close call. Certainly scalp hair grows longer. 

They have very similar growth rate.  I have not seen much difference in the past with my clients.