There's also the question of what character class you're comparing and whether or not outside sources (a.k.a gear and buffs) should be factored in.
Using just the PHB for both systems.
For example, a 30th level 4e fighter PC using the gear he started off with at 1st level is STILL a powerful force with regard to say his 15th level self that HAS appropriate level gear and in comparison to the range of opponents at the EPIC tier (basically monsters of level 20-30)
Conversely, a 20th level fighter in 3.x using his 1st level stuff I don't think actually has a chance versus his 10th level self that does have appropriate level gear. Similarly, many of the CR monsters of level 13-20 are going to have a field day with our 20th level fighter with only 1st level gear.
Worse is what would happen if the lower level fighter had access to the level appropriate buffs that would be expected (level 15 inspiring warlord and level 10 cleric respectively). Both of the endgame fighters are looking at a much decreased rate of survival if buffs are taken into account but much more so for the 3.x fighter.
This basically applies to any of the martial classes as using just the PHB, most of their power comes from outside sources.
Then there's the Stamina vs Nova question.
Pretty much impossible to exhaust the personal resources of a 30th level wizard in 4e. Even if said wizard ran out of dailies, as long as they get a 5 minute breather, they are still a force to be reckoned with in comparison to the monsters of the epic tier. In fact, the wizard shouldn't even nead his dailies to put the smack down on the critters of level 20-27 IMO.
However, the 30th level wizard in 4e can't spike/NOVA his output to such an extent that he could solo say a 35th level monster (barring some orbwizard cheese)
This is in direct contrast to the 3.x version. A 20th level wizard can easily solo a 25th level monster if said wizard has their full slots available to them. Of course, the wizard could be ganked by the local village militia he started back at 1st level if the wizard ever ran out of juice.