Regular D&D is killing monsters and taking their stuff.
Planescape, not so much. You can't kill all the monsters you meet, because there's always something bigger than you. Even the gods have forces far above them that they can't touch. And that's not the goal, anyway.
In Planescape, belief is more important than treasure. Does the monster share in your philosophy at all? And I don't mean alignment - philosophical guilds can have strange bedfellows. Maybe your mission is to recruit the monster into your sect or faction. Maybe the mission is to convince it its beliefs are wrong to prevent the town it's mayor of from sliding into another plane. Maybe your mission is to prevent some other group from gaining its philosophical allegiance. Maybe you're there to blackmail the monster, or shut down its business, or recover some abstract concept that it stole, like the bravery of the Lion Lord.
The base concept of the campaign is belief is power. It's about the struggle, or kriegstanz (war-dance) between the fifteen factions and innumerable lesser sects, between good and evil and law and chaos and good and chaos and evil and law and fire and water and light and shadow and earth and sky and life and death and death and earth and evil and earth and balance, balance, balance. That's the primary dynamic of Planescape proper: ideals, ideas, forces, and alignments, competing theories of the meaning of existence struggling for supremacy using methods both noble and not-so-noble.
Belief can make gods. Belief can unmake them. Belief can change the shape of the cosmology or preserve it.
What else? The rule of threes: between any duality or extremes there is a middle ground, a balance, a synthesis. Or as a running theme: three encounters, three aspects of every situation, three solutions to every problem, three possible endings to every adventure.
Center of all: no place in the multiverse is more important than any other. In an infinity, every point is the center. Wherever you go, there you are. Your belief is just as valid as that of gods and demons, just as powerful. No matter how strong you get, there's still stronger things all the way up.
Unity of rings: things return toward their source. Evil turns on itself. Good deeds come back to you. Life and death and the wheel of alignments and the elements are all part of one cycle, each feeding the other, all ultimately part of the same ring. Events are their own causes, as often as not.
That's not the only way you can play Planescape, of course. Maybe you'd rather turn the focus away from the kriegstanz and more toward exotic landscapes and strange addictions and alien beings and daring genre-mixing. We won't judge you, honest.
Yes... this is me... the person- I mean DM that he's talking about... It's not that I don't like planescape- actually it confused the hell outta me when I saw Sigil in the DM's guide, it's that I'm not quiet sure if there is really any difference between the two- or at least any differences that can't be argueable (is that even a word?)... so if someone could give me a few differences it would help me tremendously...
and yes when we play, it's usually a wierd mix of Fidrikon's ideas and mine, so we do use what little we have of Planscape...
^_^