I have never fought the Ender Dragon or the Wither. However, through Creative Mode in Minecraft PS3 recently, I got a little "practice" on what the Wither can do. I practiced building the Wither while also seeing what he can do. Basically, all he does is just kill off mobs and ruin structures. I put the Wither in a number of my cities, and he'd go straight after any passive mob in sight. The Wither would also damage any sort of structures in sight. He did damage to a number of buildings in some of my Creative worlds in Minecraft PS3. If there were more realistic physics in Minecraft, some of those structures damaged by the Wither would have been collapsed buildings and massive fires. As far as fighting the Wither goes, STAY ON HIM! If you let him go or if you lose track of him, he only gets stronger. You can probably get in some sword hits if you're good enough. One time I set up the Wither, I didn't finish him off... an Iron Golem in one of my cities finished him off!
The key to this is that I played in Creative Mode setting up the Wither. So I am not as experienced with facing the Wither in any mode besides Creative. I still have yet to say I've been to The End or faced the Ender Dragon. It was still pretty scary to fight the Wither, even in Creative Mode.