I'd say the two fields are very different. In the case of NLP - they watched very successful therapists in the 1970s, noticed some common themes, and extracted out a model. So for example, Milton Erickson would tell artfully vague stories to his clients, which were clever metaphors for healing, tailored to the individual. It's difficult to run scientific experiments to prove the efficacy of this - it depends on the skill of the practitioner and every client will need something different, so flexibility is key, not replicability of a technique which can be codified and taught.

CBT on the other hand, definitely ticks all the evidential boxes.

I think the two can be complementary - CBT has strong evidence for success, but maybe, the codified, procedural nature of it limits it somehow.

An NLP practitioner could try something completely different outside of any rule book if the client wasn't responding to something.

Anyway, I don't have a horse in this race, just a very curious lay-person with a few favourite classic books on these subjects.