I think it's hard to say, because we can't really quantify what a "greater" impact looks like in this case. Since Montag doesn't transform himself from a believer to a dissident overnight, we have to view his character arc in its entirety, and since, like any good story, the plot is constructed in such a way that each element contributes toward the outcome, we could argue that every element is equally important in that outcome, whether internal or external in origin. It would be pretty clear cut if Montag simply woke up one day and had an epiphany that everything about his life was wrong, but this isn't the case.
By "external" I'm assuming that we mean anything that is not already an intrinsic part of Montag's identity or body. This is important because, for example, the books are external to Montag but their effect is largely internal - Montag gains a meaning from them that may be different from the meaning that anyone else does. In this way, I think many external elements can be largely glossed of their own meanings, and many influences can be gauged on the way Montag reacts to them internally. Another good example are Beatty's arguments, which are as important for the way they influence the reader as the way they influence Montag.
I think there's a combination of both elements, beginning with Clarisse's conversation as the instigatory external element, but the greatest impact is largely from internal factors. Even from the first chapter, we can see that Montag struggles to veil his own internal discontent - his reflections on being happy (or not) and his thoughts on how disposable people have become. Without articulating this too far, I would say that Montag had to be a fundamentally good, moralistic or skeptical person with the right kind of metacognitive skills to successfully make the transition to a free-thinking life in the first place. If he had lacked these qualities, no amount of external influence would be able to free him without simultaneously replacing one set of unthinking values with another; Montag would have been just as much a blind follower of the dissident mindset as he was of the status quo.