I'm on the Shivering Isles main quest, but I'm not sure which of the two I should pick. With http://www.gamesas.com/topic/1459738-journal-of-a-time-lord-in-cyrodiil/ I'm more inclined towards Dementia but what are the benefits and drawbacks of either?

There are two places that I recall picking between Mania and Dementia.

1. One quest had to do with which fire was to be lit. (The difference is reward.)

2. Which one to assume the Duchess/Duke position. As I recall, Dementia's quest involved murder (the way the game looks at) while Mania's "only" requires poisoning food. It comes down to the murder question because of the Dark Brotherhood and your intentions whether or not to join. If your character is already Dark Brotherhood, then it won't matter all that much as the player gets promoted at the end of the quest line.