|The big green ones.|
As you can see, the difference between the Death Star's super laser and a stellar converter is that while the former blows a planet up, the latter busts right through it and causes the planet to break apart. Another difference: you can build a stellar converter on each of your planets, to bolster its defense should an enemy fleet come a knocking. You can also use converters in ship combat and even outfit your Doom Stars with multiple ones - I think the max is eight per ship. Per ship. Mamma Mia!
It's use in-game involves capturing an enemy colony world and if any of your DS's are packing a converter, you're given the option of either taking the planet or breaking it. Most of the time, I'd take the planet, especially if it was a good one (ultra-rich, good climate and size. Basically, not a shithole), but I would occasionally break it. Usually, it would be a planet with pisspoor mineral wealth, horrible climate, or otherwise not worth terraforming into something decent. Plus, it's nice not being a genocidal maniac.
Pictures via Master of Orion 2 Strategy and Giant Bomb.