With RuneQuest, I emphasized challenging adventure. I didn't understand Glorantha well enough to run an immersive cultural campaign, and the hard-edged mechanics lent themselves to exploration, challenge, and combat.
With Call of Cthulhu (as with Tucholka's Stalking the Night Fantastic), I emphasized mysteries. The PCs had huge dichotomies between their mundane lives as professors and journalists and their "alter egos" as occult investigators. Thus, their mundane lives got short shrift. In Glorantha, a PC could relate to family and society as an adventurer, so familial and social content could be part of the adventurer's life. In CoC, I didn't feel any urge to bring the mundane aspects of a character's life onto the stage.
With Ars Magica, I ran the cultural game that I had wanted RuneQuest to be. Mark Rein-Hagen and I built the game to encourage interaction among characters by their social roles: wizard to wizard, house to house, Order of Hermes to the Dominion, wizard to grog, wizard to companion, master to apprentice, etc. Plus, we had the technical mechanics for hard-edged combats and challenges, so we could switch from social mode to adventure mode and back. With some success, I tried to make Ars Magica the game that I had wished RuneQuest had been. (I understand that RQ was such a game for those who had mastered the background material. For me RuneQuest's problem was more packaging and presentation than it was content of the game as a whole.)
I designed Over the Edge to be crazy and spontaneous, so that's how I ran it. I'd generally mix alcohol, caffeine, and nicotine to get my head right for OTE. I invented whatever came to mind as we played, and wound up generating dozens of weird clues to uninvented mysteries, many of which the players never followed up. The setting was a challenge enough, so I didn't feel I needed to present the players with hard-edged combat challenges. There were plenty of fights, but the challenge was to get into the right fights more than it was to win a particular fight.
EVERWAY was also spontaneous, but its imagery was more wondrous and less emotionally and mentally violent. Some of the fun was solving problems, but a lot was exploring a new setting through a colorful persona. The subjective mechanic doesn't invite hard-edged combat challenges, so there weren't many. (Or, I wanted a game that didn't rely on hard-edged combat challenges, so the game mechanics didn't support them.) The challenge was to understand a new setting and to invent a good response to it.
My latest D&D campaign runs on the dichotomy between righteous heroes vanquishing evil on one hand and the threat of utter destruction on the other. In order to make the threat of utter destruction real, I don't fudge dice rolls for players. The players understand that the risks their characters take are real. I sort of wish that a PC had been permanently killed early on to get the players used to the idea. Now, after almost two years, a permanent PC death would come as quite a shock to the player group. [Update: Three permanent PC deaths came in rapid succession as the party tried again and again to take on the Church of Hell in Vindle. This loss was quite a shock to the gaming group.]
The setting, reconquest of a fallen land, allowed for two sorts of campaigns: a violent, action-oriented campaign in which the PCs would sometimes also encounter characters embodying strange and marvelous cultures, or a culture-oriented campaign in which the PCs would sometimes also encounter combat threats. The players demonstrated a marked appreciation for the "strike team" model of play, and that's been a lot of fun. Still, there's plenty of weird character and culture.
While irony has been a defining feature of many of my campaigns, Elysombra is noteworthy for its lack of moral ambiguity. Just because the PCs believe that their people are specially favored in the eyes of the One True God, for example, doesn't mean that they're not.
My hypothetical Gamma World d20 campaign would be in some ways the opposite of Elysombra and somewhat a reaction to it. It would be non-essential (like the "real" world) rather than essentialist (as Elysombra is, where "evil" has an objective meaning). There would be no "alignment," and no (real) deities. And it would be highly random. We designed the new D&D to be dependable, with clear guidelines for threat levels of monsters, proper amounts of treasure, etc. It's meant to be playable for years, with tools for the DM to keep the game from stalling (from too many PC deaths and setbacks) or spiraling out of control (from too-rich rewards). GW would not be that game. It would be random mutations, random encounters, and random rewards. PCs might hit it big with a lucky find (a death ray rifle lying in the dirt) or get wiped out with a bad roll (when a disintegrator grenade malfunctions).
I doubt such a high-flux game would last as long as a D&D campaign could, but it would be a welcome change of pace.