Analyze to improvise! By taking a closer look at what's going on, a piece may have a logical next step, whether that's inserting a secondary dominant to conjoin two parts or introducing an off-kilter rhythm to induce tension. Analyzing the piece to see what's needed can then open doors in improvisation that might not have opened otherwise.

I reject the false binary, so neither option reflects what I do. The best creative experiences I've had have involved a free-flowing, every-exchanging, ever-reinforcing, ever-iterating combination of the two, such that it is nearly impossible to separate them. The theory concepts you know just become part of the materials with which you are improvising.