How did hamilton's and jefferson's different personal styles affect the ways they carried out their feud

If you meant political style;
So Alexander Hamilton was a Federalist, actually he was the founder of the Federalist party. The ideas were more liberal. He was against slavery in all its forms.

Thomas Jefferson on the other hand was a Democratic- Republican, actually he was the founder of the Democratic-Republican party. His ideas were more conservative and he wasn’t against or for slavery, His ideas always remained neutral.

If you meant like actual style;

Hamilton was a very fashionable man, who often was seen wearing his glasses. His suits were tailored and usually dark colored, which was odd for a man of his financial standings. Often times people would make jokes that he was dressing like royalty, which wasn’t far off since it was almost identical to the clothing that George Washington had.

Thomas Jefferson was rather ill mannered when it came to fashion.