They were obviously quite _____ to watch.
The adjectives thrilling and content are different types of adjective. In the OP's examples, these adjectives are complements of the verb BE.
Importantly, both of these types of adjective can be followed by infinitives.
thrilling to watch
content to watch
Notice that these infinitives are really CLAUSES. We can understand them as having Subjects or Objects and so forth.
So in each sentence there is a main verb which has a Subject and there is an infinitival clause. We can understand that clause as having its own Subjects and Objects (or other Complements).
The adjective thrilling takes HOLLOW CLAUSES. This means that we understand the Subject of the main verb to be the Object of the infinitive clause:
- The acrobats were [thrilling to watch]
means something like:
- The acrobats1 were [thrilling for someone to watch ___1 ].
We could also show the sentence like this:
- The acrobats1 were [thrilling for someone to watch them1 ]
The adjective content does not take hollow clauses. It is a CONTROL ADJECTIVE. This means that we interpret the Subject of the main verb as the Subject of the infinitival clause (not the Object). We understand it like this
- The audience was content to watch
means something like:
- The audience1 was [content for ___1 to watch something] .
We could also show it like this:
- The audience1 were [content for the audience1 to watch something].
The Original Poster's question
The Original Poster's suspicions are kind of justified. Both answers could work well here if the sentence was on its own. Now that we have the context for the sentence though, it's clear that content would not work here. The reason is, we presume, that the people are going to watch the dancers. The dancers aren't going to watch anybody else. Notice more importantly that if content took hollow clauses that this sentence would be ok. It would mean:
- *They1 were content for somebody to watch _____1. (incorrect interpretation of the sentence)
Or, in other words:
- *They1 were content for somebody to watch them1. (incorrect interpretation of the sentence)
Of course, content is a control adjective and the interpretations above are not correct.
It might be worth mentioning that some adjectives can work in hollow constructions or as control adjectives. So if you go to a cannibal's house, be careful how you answer this question: