Champions Online uses the type of quest structure that's present in games like...well, World of ********. Everquest. That kind of model. You have NPC quest givers you must visit in person to start and end quests. Most quest activity takes place on a large open world map, which means other players may be competing with you for the same spawns.
In Star Trek Online, you can get quests from a menu - you do not need to physically visit NPCs. All combat takes place within instanced locations. This is more like Cryptic's first game, City of Heroes.
Here's the thing. While what Champions has feels more like an MMO, it's actually bad for storytelling. Most content in Champions boils down to 'Go to location X' and 'Kill Y number of enemies'. Or 'Loot X number of item drops from NPC corpses'. This is bog standard MMO fare. It gets boring real fast.
Star Trek Online has fewer quests overall, but the story and dialogue in each are more fully fleshed out. The instanced locations let the environment vary more, and the developers can get more creative with spawns, scripted events, and mission mechanics.
There are pros and cons to both approaches. It is possible to compromise - Champions does have some Star Trek Online-style instanced missions. But very few. Note that these instanced missions in Champions...are considered by players to be the best content in the game. The Champions players want more of this, not more running around looting corpses.
What I'm hoping is that Genesis matures to the point where it could reasonably generate an entire star system with several overlapping missions at once.