So amumu's ultimate was changed, he had a bug where he rooted champs and they couldn't auto attack.

After this latest patch I played Amumu Jungle, and I popped my ult on Darius and Lux, to buy time for my team mates to arrive (I got caught counter jungling >.>). When I ulted, it rooted Lux, but darius was still able to ult me in return, even though he was standing a little bit away from me, and was suppose to be rooted.

Does amumu's ult no longer prevent them from using abilities? Wasn't it suppose to be like a stun/Root?

You were always able to use abilities in Amumu's ult, I believe, you just couldn't auto-attack and move. Now, I'm not sure about being able to use gapclosers, though.

Amumu ult does not stop ability usage and Darius would be able to pull Q and ult. Darius ult can ult in other root forms as well such as Ryze W.

Its not a problem with amumu's ult.

http://www.surrenderat20.net/2013/01/13-pbe-update.html

According to this site, that change on Amumu's ult was intended. Players can now use basic attacks in Amumu's ult.

It wasn't a bug. It used to prevent autoattacks - stated in the description.

The bug with Darius is likely either (a) timing, or (b) an issue with whether his ultimate is classified as a gap closer.
(a) Currently, any two abilities that go off at the same time will both go off. Ezreal vs Blitzcrank is perhaps the most common... or Ezreal vs any CC.
(b) Snares only stop "movement" abilities. It's possible that Darius' ultimate isn't classified as a movement ability, like Bandage Toss and Zenith Blade (which can both be used during snares).

To the best of my knowledge, darius's ult doesn't move him. Additionally, it makes sense that amumu's bandage toss and leona's zenith blade would work through snares because the usage of the ability isn't what moves them, but an effect of the ability causing them to move.

You can somewhat see this as the reason why knockbacks work on opponents who are snared, since an effect of the ability is what moves the target.

Root means it prevents any abilities that use movement. So if your rooted any abilities like irelias dash rivens q or e, or any other similar move should be prevented. However casting and abilities like dariuses ult will not move him. Its stupid that they are applying this to him. He was such a great champ to disrupt casts and prevent actions by other teams, but now hes only good for stopping people...

I think Riven had a glitch where she could ult through snares/stuns and still move..That was the most annoying whenever I fought her with a champ that relied on those.