I think both are grammatically correct, but:

C’est un bon avocat.

would be more natural here (in this short, isolated sentence).

I would add that there is another related form:

Il est bon avocat.

which is perfectly correct, contemporary and frequent (“c’est bon avocat” does not work at all). It is not quite the same as the other two sentences, although it is really hard for me to put my finger on what is different. It feels like this last sentence only describes a quality he has, whereas the other two speak about him being an “avocat” first, and a good one second, maybe. Hard to pinpoint, but definitely feels a bit different.