From the little kendo I did, it's both, but mostly slashing. You wouldn't so much slice them in two as open them up from shoulder to hip, if you can. If you're going for the neck though, the basic technique is throat-stabbing, not slicing the head off. If the enemy has good armor, I guess you'd have to go stabby, I can't imagine a katana can slice through good steel plates (or mail, really).

But 1) the spear is the stabby weapon of choice when not in close quarters. From horseback you'd only use the katana to slice. Certainly, you wouldn't try stabbing someone with a katana from horseback.

And 2) the Japanese mostly didn't have excellent armor. They had shitty iron, so making good steel was very expensive for them. They couldn't have mass-produced steel plate armor.

The amazing thing about katanas is not that they're better than european swords (they're not), it's that they were able to make good weapons at all out of shit-tier iron.