The UCB program would probably give you access to a wider variety of job opportunities both in tech and quant Finance due to its proximity to Silicon Valley. It seems many graduates also now go to data science roles. The market is tough, might be better to have other options apart from just Quant Finance! You can check LinkedIn for analysis. I actually think many people underuse that platform.
Some things to note though. Personally, I am not very comfortable with UCB's program being just 1yr. Some might like it but I'd love to have more time to thoroughly study..
Secondly, UCB's program is in the business school, dont really know if that helps one's chances of getting into a good Ph.D. program in the future. Many students do MFE to work not to continue towards a PhD,, but it is still worth considering.
Apart from those two things that give NYU an advantage imo, NYU Courant is well known for mathematical rigor (one of the best in the world). NYU is also in New York (which is very good if living expenses is not an issue). NY Courant has a smaller class size too. If you work hard, you will have very good opportunities to work with Professors, publish papers, these things can be helpful esp. if you want to work in Quant Research or do a PhD (could be in Fin Eng, Machine Learning, or related field) in future.
You might want to check whether you enjoy proofs, real analysis, and pure maths though...if you don't, probably better to go to UCB 'cos of grades. No point going to a good school if you don't get good grades.
Both are great programs nonetheless. I understand UCB is higher ranked on this platform but consider the things I mentioned before you make a choice.
Wish you the best.