Hi Aman, You could say that, but it has a different meaning.
In the original, neither of you have written your essay yet. In your version, you are comparing what you will write to an essay of the quality of what she typically writes.
I write better essays than she does. (Habitual) I will write a better essay than she will. (Specific future event.) I will wri
Not necessarily. It could be the case that the speaker is and always has been able to write better essays. His "can do" has never been in doubt. But he's been lazy. This time, he WILL write a better essay.