I'm thinking about calling to apologise, but I could use some more opnions on this one.

Do you want to apologise? If so, then do it, however you feel is best.

Do you NOT want to apologise? Then don't. A unfelt apology can be pretty insulting.

First, it'll obviously make you feel better.

Second, you never know--it might open up an avenue to reducing or removing your differences.

Once, when I worked at an evil non-military place, this office chief didn't like me for various reasons, and kept trying to sabotage my work. Nevermind that my work was directed by the Big Guy. One day, when I was feeling like crap from a bad cold, she called and tried to pull her usual arrogant bullshit. Up until then, I'd been coldly polite, out of respect for my boss' reputation with his employees. But this time I lost it, and told her exactly what I thought of lying, backstabbing weenies who care more for advancing their own careers than for doing their jobs . . . etc. and at length.

My office, listening, was stunned.

In the interest of internal politics, I called later and apologized for the behavior (if not the sentiment!). Oddly enough, she never tried to hinder me again, and we became sort of friends, after a fashion.

Bottom line: you've got nothing to lose by apologizing. Even if this person remains a jerk, you've still proven you're a better person by not being wantonly cruel.