As TEC it is pretty simple: Send in a fleet of Ogrovs (about 20 should do the job, though you'll probably be fine with 15 or so as well) supported by flak frigates and Hoshiko's. They turn a starbase into a scrapheap in no time.
For the Advent is is probably best to use a shiteload of Solanus Adjudicators (though they are really expensive) backed by some capitalships and a bunch of Defense vessels (a Domina or two would help as well, in case you have access to them already. The Adjudicators are much tougher than Ogrovs, so repair cruisers are less of a necessity). Additionally, you can send in some Drone Hosts with Homing Mine squadrons and have them deploy those rapidly in the gravity well (in case you have enough spare resources to spend).
Obviously, the Advent have more trouble dealing with starbases than the TEC. Also, for both factions bomber spam will help tremendously when assaulting a starbase.