This is my opinion in the difference between Hanoverians and Arabs... this is just my opinion. I owned Arab crosses as a kid.
I was disappointed in the intellectual differences between the breeds. The arabs are go getters, funny, very smart, and have big personalities. The warmbloods are duller, more like giant lap dogs, smart in their own way, funny in their own way, but not that quick wit you learn to love on an arab. The warmbloods lack the stamina arabs have, so you have to be more careful in building them up... otherwise they'll get too tired and quit on you. The hanoverians seem to naturally be more pushy. It's easily trained out of them, but every single one I've met has started off trying to physically push me around. I've never had that problem with the arabs.It's kind of like how a dog will jump on you to get affection.. they seem like that. Not malicious usually, just want affection and willing to knock you over for it.
The arab warmblood crosses I've met (just three so far) have had this weird cross of really smart and down right obstinate. To the point of being infuriating. I love arabs, but... two of them were special horses. One was almost put down because the original trainer couldn't do anything with him. He was purchased by a young girl that has done miracles with him. He's happily adjusted now, and gives his all without fuss to anyone that wants to ride him. The other two are being sold for pennies on the dollar because they are dangerous and need experienced riders. Personally, I believe the issue is that people want to treat them like dull witted warmbloods, and they aren't. You can push a warmblood around and brute force them and they'll usually let you, but try that on an arab and you'll have a fight on your hands... make the arab 16.3 and 1500lbs and it's a whole other game on your hands.
Again... totally my opinion. I like warmbloods, I just don't want to own one. :)