In fairness, Caesar was only a few years younger when he was assassinated than Sulla at his natural death, so it's not like Sulla lived to a ripe old age and Caesar didn't. But yes, there are definitely a lot of important parallels between the two. As to your question, it makes sense to think of Sulla's reforms upon taking power as being "pro-establishment," since they were essentially conservative in nature, designed to weaken the tribunes and popular assemblies so that they couldn't inspire future political upheavals, and strengthen the Senate. Caesar, on the other hand, was more anti-establishment, although it's a mistake to view him as the pro-people mirror of Sulla's pro-Senate attitude. His reforms were meant to entrench his own power and centralize the power of the state; transforming yourself into a permanent dictator in what had been a republic can only really be called anti-establishment, and Caesar was pretty much transcending the "Senate vs. people" dynamic of the previous few generations.

But it's important to remember that Sulla was a very transgressive, novel figure who violently and quickly wrenched the state through a lot of changes. Sulla was the first to march on Rome, reshaped the state as he saw fit (although he didn't try very hard to make his reforms stick the first time around), and upon coming back from war, did the same thing again, slaughtering everyone who opposed him (including a lot of the establishment) and doing more or less whatever he wanted to. While the reforms he instituted after taking power might have been pro-establishment, in other words, saying that he was pro-establishment in terms of his career and what he accomplished would imply a conservative, pro-status quo kind of attitude, and as with Caesar, that's definitely not who he was.

In short: for Caesar, both his rise to power and his actions as dictator can fairly be cast as anti-establishment; for Sulla, his rise to power (although not necessarily his entire career) and the way he wielded it was even more transgressive, but you could say that his political reforms were pro-establishment.