Of course, the real joke, in comparing the two republics, is that Rome was brought down by a liberal democrat.
Though it's inaccurate to think of Caesar as the cause for the fall of the republic. Really, it was his death that brought it about. His goal was to be a more efficient and sane Sulla and get the republic back on track. Though, to do so, there's no choice but to grab all power and shake things up. Sulla managed because he didn't trust anybody and was always surrounded by legions. Caesar was a man of the people, loved by the people, and assumed he'd be safe. And he was! It's as if we got a more aggressive FDR in office who declared himself president until everything was sorted out -- social security, the budget, healthcare, a million other reforms. So, in desperation, the Republicans had no choice but to murder him during the State of the Union address.
And then they took over.
Until, say, Truman, Eisenhower, and MacArthur staged a coup and chased them out, then maintained a tenuous dictatorial hold on all of the US except for the middle states (we're focusing on grain now) which was help by the ousted republicans. The three go on a campaign of revenge and crush the ousted Republicans. Eisenhower takes command of the west coast, Truman -- heir to the dead FDR -- takes the east coast, and MacArthur takes the grain-rich middle country and they rule as a sort of populist rump in the senate.
But then MacArthur goes insane and, seeing himself as the ultimate power, and already kind of hating Truman, makes a bid for complete control. This in the wake of Eisenhower's death, so there's a gap in the trio's power structure anyway (which, oddly, back to Rome, is exactly what happened to pit Caesar against Pompey. The situation is eerily repeated with Antony and Octavian when Lepidus dies.).
Okay, so MacArthur gets creamed (through trickery, really) and Truman takes ultimate power... Leading to a cult of personality that would thrive, in one way or another, for the next 1400 years.
So that's the fall of the Roman Republic in modern terms.
It's actually fascinating. I think we dismiss it because the west was lost after a few hundred years and historians are very lazy about categorizing the Byzantines. The truth is that Rome the empire didn't fall till the 1450's. And, for that entire time, they play-acted at being a Republic. The emperor was never emperor until the final centuries. He was head of the senate. "First Man." A title anyone could get at any time, technically. Of course, it was rigged, and awesome powers were in place for him to abuse. But, you know, on paper... The Republic never died.