The comparison doesn't have a great connotation, given that "fundamentalist" is typically an epithet, but it's not too far off in terms of the denotation.

Personally though, I would say it's more of an Exoteric / Esoteric split; conservatives seem to spend most of their effort preserving outward forms and rituals of their cultures in an effort to keep the fire going, where reactionaries see it as burnt out already and so look back for the essential (in both senses of the word) elements to spark a new one. A good example is comparing Chesterton's Catholic apology with Evola's promotion of Tradition, not to imply that you can't be a Catholic reactionary but just as an example of a differing mindset. Of course, esoterica being what it is, it's a bit tough to get a grip on and much easier to talk about than to understand fully.