As a DM who's players are at level 20, have been playing since level 1 (late-starters not withstanding), and will soon be getting to level epic tier, I enjoy these threads and comments. So far, I'm thinking that a lot of the shift from heroic to paragon to epic really depends on how the DM plays it.
Paragon tier for me meant that the players could now explore the wider world and could get into all sorts of trouble without me actually having to feed them quests. They could pick and choose what they wanted to do, and where they wanted to go.
Epic, from what I see, is a reversal back to heroic tier-style story-telling, where the players should give up some of the liberties of player choice so that the DM can really focus on the story and the progression towards the ultimate goal of the PCs, and not worry so much about the players derailing what's going on. Of course that won't work for everyone, but that's how I'm playing epic tier.
That's why epic tier is so hard to play: it relies on characters' stories and backgrounds more than any other tier, almost detrimentally. Sure you can run one-shot epic adventures, but to get to the meat of epic tier play, you need to have a developed story, characters, cast of NPCs and a villain with which you use to create the climax of your campaign.
That said, I think the best way to get epic tier to shine, story-wise, is to have everything the players are fighting for, get progressively worse right up until level 21. Level 21 is where the players can start doing stuff about all those things that went wrong before. That really makes epic tier stand out.