Pathfinder Adventure Path, Roleplaying Game Subscriber
Invulnerable Rager is popular because you're getting a strong defensive bonus basically for free. Uncanny Dodge is a really pointless ability for most barbarians; your dexterity is going to be low so the difference between flat-footed and not flat-footed is negligible. The only category of Barbarian that falls under "can, but maybe won't" for IR is the Urban Barbarian because that's the only time your dex will be high enough to get value out of Uncanny Dodge.
The value of uncanny dodge is getting improved uncanny dodge at level 5, then those pesky sneak attacks stop working unless the bad guy is 4 levels higher than you which rarely if ever happens. Basic uncanny dodge is largely useless though.