I believe that what you're dealing with is a compound predicate; i.e. you have one subject with more than one predicate. It might help to explain this first, because (a) it might not be obvious and (b) it informs the answer.
To start with, there is a dummy subject. Your real subject is the noun phrase other conspicuously terrifying moments. The two clauses contributing to your sentence, rearranged to remove the dummy subject, are
- Other conspicuously terrifying moments were during the ride. [I.e. other terrifying moments occurred/existed during the ride.]
- Other conspicuously terrifying moments were not any more terrifying than that one.
(In this analysis, the two instances of were are different verbs, coming from different contributory clauses, even if repetitive of a single verb form.)
You can also perform a similar breakdown while leaving the dummy subject intact, if that seems easier to grasp:
- There were other conspicuously terrifying moments during the ride.
- There were other conspicuously terrifying moments not any more terrifying than that one.
Combining these two sentences with but as a coordinating conjunction, you get an awkward compound sentence:
- There were other conspicuously terrifying moments during the ride, but there were other conspicuously terrifying moments during the ride not any more terrifying than that one.
Getting rid of the second instance of both the subject and were through ellipsis, you get your compound predicate:
- There were other conspicuously terrifying moments during the ride but not any more terrifying than that one.
This is different from many compound predicates in that many have two explicitly different verbs, so the second verb is not elided. Here, instead, you're faced with the same verb form in the second instance, which can be elided although the two instances differ in their sense.
And the answer is...
Regarding compound predicates, the fourteenth edition of The Chicago Manual of Style says
Preferably, the comma should not be used between the parts of a compound predicate. ... A comma may be added, however, if misapprehension or difficult reading is considered likely without such punctuation. (5.33)
So the answer seems to be that it might be considered better style not to put a comma before but in your sentence (in fact this advice is all over the internet, for example here and here), but there's no hard and fast grammar rule against it, and for such a sentence, if a comma were to aid in apprehension, you should probably put it in.
Commas are often largely a matter of style and clarity rather than of grammar per se.