First it is really hard to answer questions like "ranking" for Math Finance programs because even the oldest programs have only been around since the mid 90's. Now to compare a US program vs. an International progam makes this task even more difficult. Still... here's my attempt
Comparing the two you will find that the LBS program is offered by the business school while the Princton program is offered by the Bendheim Center for Finance. This is important because looking further into the programs you find that the LBS program is probably the most MBA'ish type Masters in Finance program out there (more so than UCB). LBS admitts those with far more work experience (6yrs vs 2 yrs) and they report average GMAT scores (675) while Princton only reports average GRE (790 Quant); note that Princton does accept the GMAT.
They are both top programs and it really depends on what you want to do with the degree, but more importantly where you want to work. If you want to work in NY you would be a fool not to go to Princton but if you want to work in Europe I would be hard pressed to discourage you from going to LBS.
So to answer your question, which is a "better brand," well, that depends on who you ask (NY or London) and what you are selling (Financial Management or Quantitative Finance).