The key is how much work gets done per clock cycle, not how many MHz or GHz a processor is running at.
If you look at cars, a V6 and a V8 engine may produce the same amount of horsepower based on design differences, but the V8 will be able to do it at a lower number of RPMs. One may push 140HP at 5000RPMs, the other may push 140HP at 6000RPMs. Now, they are both giving the same amount of power, but just because the RPMs are different doesn't bother anyone. There WILL be differences in acceleration, heat produced in the chambers, and so on, but most people don't look or care about that.
Processors work the same way, though overall computer performance has other factors. A P4, just because it runs at a higher number of MHz WILL do some things faster. Think of it in terms of doing nothing, or some very simple tasks very quickly. But as things become more complex, differences in design will start to lean toward the better design in many areas.
Another way to think about it is a fight between someone very strong, and someone very quick. If the strong person lands a hit, it will do a LOT of damage. The fast one can land a hit quicker, but it doesn't do as much. Depending on the length and rules of the fight, the strong one will win easily, but in other situations, the fast one will win easily. In the long run, it all depends on what you are doing, and how well weighted the environment is toward one or the other. The Athlon 64 is a good all-around contender, being able to win most fights in most environments. There are a few areas where the "speedy" P4 comes out on top though.
Now, there comes a point where the quick fighter just can't get any quicker, and the strong guy because of his physical build can't get any faster as well.
Of course, going forward, both AMD and Intel have decided to go with a "tag team" approach rather than bring in a new generation of fighters. Dual-core is the current direction things are going in. As with the current situation, fast vs. strong, the environment the fight happens in will play a part, but an even greater part than previously. Up to this point, we would see the P4 running out of room to grow at around the 3.6GHz range. A dual-core part can't do two cores, each at 3.6 because the power needed and heat released would be excessive and not acceptable in the market. By the same standards, the Athlon 64 at current top speeds wouldn't be acceptable for most people due to heat and power demands.
So, we will see two-core chips from both AMD and Intel, with each core slower than the current top-end processors. Due to design issues, we might see lower performance from these new dual-core processors under MOST applications. Obviously, AMD and Intel will be working on solutions to this, and it is probably why the latest AMD roadmaps don't show many increases to clockspeeds in 2005.