As Advent, the best strategy is to simply stay out of range while your strikecraft reduce the base to slag. Well, that works for every race, really, but the Advent excel at it. If it's a Vasari starbase and it comes after your carriers, I try to stay out in front until its about 1/2 health, then just let my fleet finish it.
As TEC and Vasari, I can usually just fight it out with my fleet, being careful to pull back any severely damaged ships, while my strike craft hit the repair bays. I don't think I've ever lost more than 3-4 frigates, if that.
I don't really use siege frigates. Maybe a few, but with SBs being so weak, you don't need them.