the trouble with 4e Epic play is that it just doesn't tend to feel very, well, epic. Since the opposition's numbers scale with those of the PCs, and since there aren't much in the way of fundamental game-changing elements introduced at Epic tier, you're basically just doing exactly what you were doing at Paragon tier, except adding larger numbers to your dice rolls and changing the names of the opposition.
MarkB's comments don't describe my own experience with epic 4e. The PCs aren't doing basically the same as what they were doing at Paragon tier. (The mechanical procedures of play are very similar, but the story elements are not. At Paragon, the PCs in my game were freeing a baron from the influence of his evil advisor. Now that they are epic, they are freeing the world from the influence of the dark god Torog.)MarkB's comment is very accurate - do characters really feel epic (in other genres, SuperPowerful) when their opposition's power increases in lockstep with their own?
I've heard it said that 4e epic is simply D&D with bigger numbers. You can certainly play it that way if that is what floats your boat. The game does not prevent the DM from doing that. But a failure to be epic is mostly a failure of thinking about what are the correct challenges on an epic level. The challenges at those levels need to be epic in story characteristics.
I agree with these posts - the basic procedures of play don't change in epic 4e, but some of the details of the mechanical options do. PC death avoidance is probably the most striking.I dont think the higher numbers are what make epic play. The epic...ness has to be within the story - most significantly the scale and stakes/consequences of the story.
That said one of the defining aspects of epic play in 4th ed is also the PCs ability to avoid conditions (including death!) and more readily imposing conditions on the enemy.
But most important - and underpinning those changes in mechanical options - is the underlying story. The PCs are now demigods or some equivalent thereof. The stakes are more momentous. The fate of the world hangs upon their choices!