From what I have read, it seemed like Adams was a little jealous by nature, and Hamilton was a bit impetuous and arrogant. Adams probably felt his contribution to the founding of the country commanded more respect than he got as president (Washington was a tough act to follow). Hamilton probably ran over Adams a time or two with his bias toward action, and his youthful pride, as he endeavored to serve Washington and fire up the federal engines. I haven’t read that it was any specific ideological divide (like Jefferson and Hamilton), just incompatible personalities as far as I have researched it.
Hamilton is probably, to me, the most fascinating founding father, the more I have read of him. Deeply flawed guy, and he made some policy calls I didn’t like here and there as he was basically inventing the practical institution of the federal government, but he was brave and deeply suspect of fallen human nature. That wariness, and his humble beginnings made him personally revolted by slavery and informed his advocacy for the separation of powers. He also seems to have developed into the most devout of the bunch, as he got a bit older and saw the darker side of humanism exhibited in the French Revolution.
Will take it the bank.
Thank you very much.