Several commenters suggested that I try switching my budding Warrior alt from Fury to Arms for a different experience. As it happened, I'd just finished saving up enough gold to pay for dual spec (with 1000G in the bank for cold weather flying when I need it), so I figured that there wouldn't be any harm in taking the other DPS spec for a spin before using the second slot on a tanking spec (presuming that I decide I'm brave enough to try tanking).
Superficially, the two specs have a bit in common. Arms Warriors get the famous Mortal Strike skill instead of the Fury self-healing Bloodthirst attack. Instead of waiting on a talent to proc instant-cast Slam attacks, Arms gets talents that proc instant Overpower and/or Execute attacks. Because these abilities require Battle Stance, I don't get to use Whirlwind (a staple of the Fury rotation), but I get additional tools including Thunderclap, Sweeping Strikes, Retaliation, and Bladestorm to deal with additional foes.
Regardless of how different the two are on paper, though, I find that I greatly prefer the feel of the Arms spec. The results may be similar, but it feels more interactive to be making a choice that now I want to hit multiple targets or now I want to do something that refills my health bar. With Bloodthirst and Whirlwind in the standard Fury rotation, both situations all but take care of themselves for solo content. Arms might be less effective (especially against casters, for lack of convenient access to pummel), but it feels more fun - perhaps the decreased efficiency even helps raise the difficulty from trivial to "need to pay some attention".
P.S. Also, there's nothing that I've done on any of my characters that quite compares to Bladestorm. In solo content, clicking that button makes four mobs die in the next seven seconds. The thing is on a cooldown (90 seconds, 75 with a glyph), but you shouldn't need to pull four mobs at once more often than that, and you've always got Retaliation in your back pocket if there's still mobs standing when you're done spinning around.