My first horse was a TB. My second horse was a TB. Then I got my first Arab, but always had, up to a year ago, a TB also. The difference I saw is the TB is more "business" like, the Arab more "personal". Both are very in tune with their person, the Arab is more outspoken, if you want to call it like that. More reactive, more playful. A TB, when worked every day, functions. The Arab functions also, but is always up for some entertainment.
I've also found that an Arab "works" better when I act as if he/she hadn't done anything wrong and just keep going, instead of correcting. To the point where they get over a scare or spook easily when the person simply laughs about it.