That's actually a 50% power drop from Outrage to Dragon Claw, not 20%. But yeah, the extra power really does matter against a few things. For example, CB Dragon Claw doesn't get close to a 2HKO against Hippowdon or Chesnaught, whereas Outrage with Stealth Rock down has a great chance to 2HKO the former and is a guaranteed 2HKO against the latter. Being trapped into the move sucks, so it is kinda risky, but it generally works out decently enough. If your opponent brings a Fairy into the second Outrage, then you get to switch out the next turn and preserve your Tyrantrum, and you've successfully knocked off half or more of your opponent's important Rock resist's health (i.e. a Hippowdon that switched into Outrage and back out again will be 2HKOed the next time by Head Smash, assuming Stealth Rock is down). Now, if your opponent goes to a Steel, you'll be in a pickle since you might be trapped for a third turn and be forced to take a STAB Steel attack, but that's just part of the risk/reward that has always been associated with Outrage. Besides, some Steels actually take a hefty chunk of damage from a CB Outrage, so if they're worn down enough, you might be able to 2HKO. Basically, the way I see it, the difference between Outrage is Dragon Claw is having a risky way to get past those sturdy Rock resists and having no way at all (unless you find another way to wear them down significantly beforehand).
Keep in mind that I'm mainly just referring to the Choice Band set. On Rock Polish/Dragon Dance sets, I might not even run a Dragon STAB at all myself.