Starbases can't have admiral leadership bonus, which is absolutely huge. Admirals level up faster than any other leader type, so they're frequently maximum level and giving full benefits to their ships. Because of the effect of admirals, I find that starbases will straight up lose to fleets at equal power. You should always try to go overkill with starbases; weapons upgrades and platforms in particular are critical to keeping them formidable enough to ward off enemies.

If you've got the credits and fleet capacity for it, ships are straight up superior to starbases. They're mobile and you can put admirals in charge for a power boost. There is no contest. The advantage of starbases is that they don't take up fleet capacity, cost significantly less upkeep, and provide you with hyperspace control so the enemy can't run amok in your rear worlds. On the higher difficulties where it's just straight up impossible to match the size of the AI's fleet for the first 200 years or so, starbases are basically necessary for survival. On the lower difficulties (or with scaling difficulty enabled) your economy will be strong enough to match or exceed the AI in the open field, and starbases are mostly useful as hyperspace control.

I'd also point out that power isn't additive; having 1100 power starbase and a 300 power fleet is way weaker than a single 1400 power entity. This means keeping small defensive forces to support your starbase isn't overly useful. Build defensive platforms if you want to do that.