Triangular mesh is conceptually simple, but requires many faces to approximate curved surfaces with high precision (you may be able to use subdivision surface in some cases but intersection/union in those cases are more challenging). Also, for more complicated models, floating point errors really add up and you either have to use an exact representation (which is really slow) or try some other approaches which can be robust w.r.t. errors (e.g. https://github.com/elalish/manifold but it is really hard to get right). Another disadvantage comparing with BREP is the lack of constraint solving, which I will write about it below.
SDF is nice for mathematically defined objects. They are computationally intensive, so some sdf libraries use GPU to speedup the computation. There are approaches that can speed up the evaluation, but doesn't work well if the function is not really the distance (https://github.com/curv3d/curv/blob/master/docs/shapes/Shape...).
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Constraints solving: This is a big problem with mesh-based CAD. Traditional CAD usually allows you to have under-defined constraints, and users can iteratively set constraints until the model is fully defined. There is no such a thing (yet) with mesh-based CAD. Also, we don't really have nice ways to represent constraints relative to curved surfaces because there is no curved surface in our mesh...
Also, one particular challenge with text-based (or code-based) CAD is how to select the surfaces with an ergonomic API. GUI can solve this problem but writing a good GUI is a complicated task (that I am not willing to touch).