Stations have one massive downside, and that's that they take up land. When they're close to your colony, this becomes a somewhat annoying problem because you cannot settle cities near them. Even though they physically do not take up more than one tile, your colonists must still obey the normal three-tile restriction before settling down just like with Cities. That's very troublesome if there is a nice plot of land anywhere near a Station.
Luckily, problems have solutions. You can destroy Stations with your military forces. They're way easier to trash than a major city, but they still take a few hits to bring down. They deal counterattack damage in melee, but they don't have ranged attacks. Use a melee Trooper and some ranged support to splash the Station and knock it out of your way.
Upsides: Destroying the Station frees that territory for settlements, and you get a yield bonus from taking the Station itself. In addition to that, a derelict settlement artifact is left behind. Bring an Explorer along to exploit that before anyone else can. It's a pretty good deal for the destroying party.
Neutral points: Stations are not allied with each other. You can destroy as many or as few as you like, and the other Stations won't care.
Downsides: Any colony that was trading with that Station isn't going to be too happy with you for taking out their trading partner. Avoid attacking Stations that are far away from your territory, unless you are willing to upset your rivals.