You have some wonderful thoughts and colorful words here. It needs just a little more polishing and some solid examples to punch up the points you are making.
Most readers, and your teacher especially, will know who these two men were, but I think that you ought to spell it out at least once. Use their full names, give a time reference, and the countries where they held power. It doesn't have to be grandiose, just tuck it in there-"Maximilien Robespierre rose to power in the revolution that disposed of the French Monarchy." Or something along those lines. Both men are very controversial figures. Some people hold them up as fine patriots and national heroes while other people see them as power-hungry villains.
Cromwell rose to power in the war against Charles I who wanted absolute power. He quickly proved himself by reforming the soldiers into the New Model Army, which won the Civil War.
Expand on this point just a little bit. "Cromwell rose to power as a military leader during the English Civil Wars. His men greatly admired him for his martial instinct. Cromwell's belief that he had divine guidance and a God-given right to rule England drove his reforms of the army and led ultimately to the execution of Charles I." I think you also need to address here the dichotomy of the man. He was a national hero to some, but also a tyrant. His body may have been buried with honors at Westminster Abbey, but it was dug up and desecrated a few years later. It doesn't seem right to talk about Cromwell without mentioned his campaign against the Irish Catholics. Maybe add something like this: "Cromwell pursued the Irish Catholics with a genocidal brutality. Cromwell himself denied this claiming that he only waged war with those bearing arms." But . . . being the multifaceted man that he was, Cromwell also made strides in England against religious persecution. He even invited the Jews back to England after a long banishment.
Similarly, Robespierre ruled rather well at first and did lots of helpful things such as creating a new calendar and driving out the church.
Hmmm . . . he did lots of helpful things like creating a new calendar and driving out the church? The French Republican calendar was a rather odd and confusing thing. There were ten days in a week, ten "hour" days (the whole clock became deciminalized), and renaming/renumbering the years. Besides, Robespierre had very little to do with its creation. The value of driving out the church would be subjective. The Catholic Church was restored in France in 1801. You might want to add to this paragraph to show the rise to power, the ability of power to corrupt, and the results of that power . . ."In Robespierre's early rule, he was called "incorruptible" by his peers, who admired his virtue and steadfast dedication to the revolutionary cause. Robespierre wielded his power in an internal purge of personal enemies and enemies of the state."
Afterwards, his rule was overthrown and constitutional monarchy was declared.
Not exactly. Upon Oliver Cromwell's death in 1658, he was succeeded by his son although the office of Lord Protector was not hereditary. The English government was chaotic without Cromwell's strong leadership. Charles II was invited to return to England and assume the throne of his disposed father in the restoration of the monarchy.
And now, onto how they lost their power.
This is a pretty informal transition for an essay. A little too conversational in tone. Reword it to something like this: "Cromwell was able to maintain his rule until his death from malarial fever in 1658. Robespierre, on the other hand, met the fate he had inflicted on so many others when guillotined in 1749 by his political enemies."
After a failed attempt to shoot himself
Robespierre didn't fail to shoot himself, but he did not kill himself like he intended. Semantics. He shot himself in the jaw and was unconscious as the arresting party arrived. You don't need a lot of detail here, but you should correct this to mirror the truth in case your teacher is a stickler for detail.
And after comparing all factors of their rule, you have to agree that Cromwell is a better and more effective leader. Ask yourself this. Which one would you prefer? A joyless and grim life or a life lived constantly in fear of not being able to see the next morn?
You'll need to strengthen this, but you already knew that. Conclusions can be difficult. I wouldn't quote Chinese or American proverbs-they will read like fluff instead of supporting your arguments. Few men in history were as controversial as Cromwell and Robespierre. Do you have to pick one to support or can you say that they were both dichotomous in their rule? Hmmmm . . . Cromwell put an end to England's bloody civil wars, but that is the only good thing I can think of that came out of his tenure (he let the Jews back into England, but in this essay, that is a very minor point or not even a point at all) . . . I am not sure what other evidence you can come up with to support the concept that he was better than Robespierre . . . I am also not sure which man was responsible for more deaths, but I'd put my money on Cromwell.