Is it appropriate to mention that another school awarded more aid when writing an appeal letter, or is it better to leave that fact out?
That is unlikely to sway them much as each university uses its own formula. This may work is you are applying between two UC campuses, or say between Smith and Mt Holyoke, i.e. peer institutions. That said, any appeal will need to be supported by new evidence that demonstrates that the original calculation was wrong or that they overlooked something.