Note: When I played the board game it was using up to 3055 tech lvl 2 rules, so keep in mind they didn't have all these fancy-schmancy autocannon types/ammo yet.
I think one of my favorite weapons of all time for IS was the LBX AC-10. Oddly enough, it weighs one ton less than the standard counterpart, but the other calibers of LBX autocannon do not (though all the LBXes benefit from being one crit smaller and one hex longer ranged I believe). Since the LBX 10 was also a ton lighter, that made it appealing. Giving it a ton of standard ammo and a ton of submunition ammo gave a mech a nice degree of versatility.
I've heard a lot of arguments on why ACs are inferior. However on the inner sphere end of things I honestly don't think they're that bad. I don't know why, but AC's just "feel" old school to me. An IS ERPPC is going to blow way more heat for the same damage for more range. A Gauss rifle for IS is a big investment in space and weight, has a min range and makes the pilot suffer a hit if the rifle is destroyed, something kind of easy to do since it hogs up so many crit slots. LRMs are nice but have a pesky minimum range which really mitigates firing them at short range to get easier to-hit rolls. And of course virtually every weapon could be replaced by batteries of medium lasers but that's beside the point.
Even the smaller calibers, AC/5 and AC/2 respectively are even less popular. LBX-AC2 though has really good range and you never know if you might KO a pilot with a lucky headshot (cluster rounds definitely make that a bit easier).
Still, for what you get I think LBX autocannon have a good heat-damage ratio (and a weight-range ratio, even though many might disagree).