Well the most obvious parallels are the Bene Gessirit/White Tower and the Fremen/Aiel.
In the BG and WT parallel you have a group women (and women only) who have abilities others don't understand. A secret society deemed to be 'witches' who are heavily into politics and the aquisition of knowledge. They also both place themselves into the position of councilor to royalty to further their plans. The main difference is that the WT doesn't seem to have a specific overall plan for the direction humanity should take. They're more rooted in the present.
The Fremen/Aiel parallel is tremendous. Both are a desert dwelling people who are an outcast/warrior race. They both come from peaceful backgrounds and were driven to their current place by cataclysm. Both groups are incredible fighters and both have an intricate cultural system of beliefs that is very different from all other known cultures. Neither group accepts outsiders easily. Both believe a time of testing will occur when they will be raised up or destroyed.
WoT doesn't use many of the other aspects of Dune (CHAOM, the Landsraad, Bene Telulax (sp), Ix, Butlarian Jihad, etc... but I think it's fair to say that Herberts command of sub-plot is almost on par with Jordans but is not as evocative when dealing with individuals. Herberts series is more cerebral, dealing with politics, spirituality and the basics concepts of evolution within all relationships. It's not an easy read the first time.
I know alot of people who couldn't make it past the first 100 pages as Herbert tries to immerse you in the world and culture before getting to the main plot. This immersion pays off later when you see the contrast the Fremen culture presents when Paul is thrown into it.
in Dune, the Fremen used devices to gave words certain power... say a word while wearing this device, and aiming the power and it destroys *explodes* something... and they had a certain tone of voice, where if used, you could make someone do anything, like compulsion..