In the sciences/math, obviously the word means to produce a 'complex', i.e. where 'complex' is a noun, not an adjective..
That set aside, I think, when you use it as a *verb* to say (A) "he is complicating the topic", and (B) "he is complexifying the topic", the difference may perhaps be negligible, unless you mean that in the case of (A) it is a largely negative connotation, i.e he is just making things look difficult and in the case of (B) he is adding layers of sophisticated arguments to explain how things are not as simple as they look.
So, an argument that goes "hey ,if you want to got to the party, first find a blue dress, and even with a blue dress you need a headband with tiger paws printed on it, and then you need to sub bathe for 15 hours 65 mins before you go" could be taking as complicating matters..
But, an argument that says "geopolitics in this part of the world must be accounted for/analysed with the help of a multiple contributing factors. For one, one must keep in mind the treaty of XYZ, another thing is the theory of ABC"...this could be a case where the author has added complexity (complexity not as a negative word but as a word to mean more analytical layers) to the argument and hence 'complexified' the situation. Obviously in this case you cant say he has complicated the situation.
That could be one potential way of using the terms differently, not the only way, or the definitive way, but just one possible way