I think that the while the game stays relatively balanced all the way up to 20th level, it does get more complex. The problem with high level PCs isn't their power as much as it is with their options; they've got so many resources that it can be difficult to plan challenging adventures for them.
Of course... anything that the PCs come up with, the DM can use on his side of the screen as well.
And, don't underestimate the power of foresight... if you know what your players will do, hit them where they aren't looking. Use the terrain to your advantage, for example. On average, my finding (after 25 years of running games) is that most parties hold up very well when you hit them with an encounter they are geared for, hold up okay if they have sort of thought through that type of encounter, and completely loose it when you disrupt their core capabilities. Sucker them into committing before you change the game on them...