The way I see it, the difference between Sulla and Caesar is that one restored the republic in the end, and the other didn't (or didn't have the time to). I don't mean to say that Sulla was in any way better than Caesar - In fact, he was far, far worse - but the Republic did survive him, and many of his reforms were repelled after his death. After Caesar's death, the Republic existed in name only because, as you said, the Second Triumvirate immediately followed, which was as much democratic as Sulla's dictatorship. Basically, after Sulla there was still a Republic to return to, while Caesar paved the path for nothing but dictatorship.
I think it's poignant that what we call the "second" Triumvirate was an official commission, while the first one was an informal agreement among powerful individuals - the fact that Caesar and his merry companions had to do it in secret is meaningful proof that the Republic was still "somewhat" functional, while it had already been irremediably ruined by the time the second Triumvirate was born.
This entire conversation is, of course, a huge oversimplification of far, far more complex historical events that I would certainly not be able to summarize in a shitty Lemmy post: looking for a single person responsible for the collapse of an entire political system is an exercise in futility; as futile as pointing to THE cause for the fall of the Roman empire.
That being said, it's impossible NOT to include Caesar (and Sulla, and many others) among those responsible, and Caesar would certainly be one of the prime suspects, since he was the one on the crime scene when the Republic was found dead.
EDIT: I didn't mean "Shitty Lemmy post" but "Shitty Lemmy comment', ie. I was talking about my own comment. I love your memes, I would never insult you :)