Personally, I would choose Courant over UCLA.
Living in NY is a big plus in my opinion. NY is a great city to explore. I study at Columbia MFE and I go downtown to drink on average twice a week. The smaller class size is nice. It gives it a more cohesive cohort experience. I think apart from socially, the smaller class size doesn't matter. If you want to get to know your professors you still can in a class size of 100+ and I do not know how much 'personal attention' career services will give you. I am also a math nerd and think I would enjoy the classes there.
And not to discredit UCLA, which is a great school, I know graduates from their last class working for as large IBs, S&P, Blackrock, and Jane Street. One of my best friends just graduated UCLA MFE! You hit it on the mark that since UCLA is tied with Anderson their students get a lot more resources put towards them despite their class size. We have only one dedicated career service member for FE as a comparison. UCLA also has great sports teams to go watch while you are there.
Chintan is correct to say that it's hard to objectively say which is better. Both programs Can create strong quants/traders it really depends on what environment you want to be in and what you do during it. I know a FE degree is a professional choice but try not to think myopically. An FE degree is way more than what you learn in the classroom. It will be the peers you meet, the professors you look up to, the city you get to explore, the place you like to study, and the pride that comes with being a Bruin or a Bobcat.
Good Luck!