I have to do an essay on the similarities between the two but am finding it extremely difficult to do so without being very general/vague.
Well it depends on when you examine them. They agreed more early on but during their time in Washington's administration they came to disagree over much.
What I would say is that early on Jefferson saw the need for some kind of federal power because of the inability of the Continental Congress to pass a strong budget or collect money or recruit soldiers. Hamilton would have agreed; he served in the field during the Revolution and saw first hand the results of the weakness of the Congress. So I think they agreed on that.
Both were excellent writers. Both had extra-marital affairs. Both revered Washington (Jefferson did abandon Washington for a while, but by the end of his life had come to regard Washington as the Father of the nation). So I think in that sense they were similar as well. But they were quite different in their political positions, and I find it hard to find similarities between the two there. Hamilton was a federalist and Jefferson was a democrat. I suppose what you could say is they were equally pig headed in their inability to see the other point of view.