The Castle is basically Battle Tower but if you increase your opponents Pokemon by 5 level for the first 4 streaks (apart from against the brain) you'll end up with enough points to skip the remaining 2 streaks and have items and reduced oponents for the final Brain Battle. The points are annoying and you can't have your own items in there for a while.
The Battle Arcade is just a Battle Tower with even more hax. You can use it your advantage but you need a quick reactions. You can't use your own items, they are random and you get less points from it.
The Battle Hall is annoying. I keep losing to Focus Sashes. I like the concept but doing all 170 is way too hard. I've got to 118 but more Sashes. It's strange because you can do the ones you're weak to easily but something random will stop you.
The Battle Factory is the best. It may be the hardest but it's the most fun as there are so many options and taking you opponents Pokemon almost as a prize is cool. My first Battle against Thornton was heart-stoppingly close:
My battle against Thornton
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