I normally try to stay away from these kinds of questions; watches are like shoes, they're incredibly personal. I really can't make a suggestion for you. However, I have such strong feelings about these two watches that I wanted to share my thoughts.
I saw the Breguet La Tradition Tourbillon about a year ago and I've said in the past that I was a bit disappointed with the Breguet La Tradition Tourbillon; the watch was much too thick, the crystal was much too thick, the chain didn't look delicate enough - it looked too crude, and overall the watch wore much larger on the wrist than I would've liked it to. The big balance wheel on the Breguet La Tradition Tourbillon is a plus. Tourbillons are most effective when the balance wheel "has a large moment of inertia" or when the balance wheel is large. Overall, I would say; I love the concept of the Breguet La Tradition Tourbillon, but I didn't love the watch as much as I loved the concept of it (don't get me wrong, I like this piece, I even think it is perhaps the best Breguet on the market).
On the other hand, the Lange One Tourbillon is a nice watch. There is nothing wrong with the Lange One Tourbillon (perhaps the balance wheel and cage is a bit on the small side), but there's nothing terribly fantastic about the Lange One Tourbillon when compared to other tourbillons (yes, it is beautiful, it looks fantastic on the wrist, it is practical, it has a hacking second hand). However, overall, I'm not terribly intrigued by the Lange One Tourbillon.
Between the two watches that you mentioned, I would acquire the Breguet La Tradition Tourbillon, however...
If it were my money. Honestly, I would try to acquire the Richard Lange Pour Le Merite, the one with the chain and fusee and the enamel dial (a problematic enamel dial apparently). Only the rose gold models are available currently, but this is a watch that is truly unique and represents something.
Feel free to PM me if you have further inquiries about my rationale.