Tarkin put it best when he said
Fear will keep the local systems in line. Fear of this battle station.
Star Wars: Episode IV A New Hope
The Death Stars' superlaser is not intended to destroy planets so much as provide a credible threat that those planets can be destroyed. Think of the nuclear arsenals of countries like the United States and the former Soviet Union: these arsenals are more than enough to kill everyone on Earth, but no one wants to actually use them. They exist only to prevent other countries from launching an attack, lest they invite a retaliatory nuclear attack on themselves.
The use of the Death Star superlaser on Alderaan was intended mainly to demonstrate that the Empire possessed the ability to destroy planets. It is similar to how the atomic bombs dropped by the U.S. on Japan in World War II were partially intended to demonstrate to Japan (and the rest of the world) that the U.S. possessed such a powerful weapon. With Alderaan a demonstration of the Empire's capabilities, the Death Star would theoretically never need to destroy a planet again.
The Death Star is so huge that it is also theoretically invulnerable to even the largest Rebel fleet, whereas Star Destroyers are small enough that they can be destroyed by Rebel capital ships:
Tagge: Until this battle station is fully operational we are vulnerable. The Rebel Alliance is too well equipped. They're more dangerous than you realize.
Motti: Dangerous to your starfleet, Commander, not to this battle station!
Star Wars: Episode IV A New Hope
The Empire of course did not realize the first Death Star had a vulnerable thermal exhaust port which would allow a starfighter to destroy the whole station. Theoretically, the completed second Death Star would be invulnerable to both starfighters and capital ships.
The Death Stars are also mobile battle stations which house hundreds of turbolasers to be used against enemy capital ships, innumerable troops for deployment on planets, any supplies necessary for military campaigns, etc. It's essentially a massive Imperial base/fortress, except that it's mobile and capable of hyperspace travel.
As seen at the Battle of Endor, the second Death Star's superlaser was accurate enough and could be fired quickly enough to be used against enemy capital ships (in addition to all the turbolasers on the station). The Battle of Endor had two primary purposes from the Empire's perspective, one of which was to take advantage of this capability of the Death Star and destroy the entire Rebel fleet (the other to turn Luke to the dark side). The Death Star systematically destroyed the Rebel fleet with its superlaser:
...while the Imperial Starfleet, originally hidden on the far side of the Endor moon, pinned down the Rebel fleet:
