Neither will be better or worse as far as the career of investment banking goes, and you don't need to do a highly mathematical degree at al for that sector - IBanking doesn't involve much maths beyond GCSE level, that kind of stuff is done by quants, not IBanking analysts.
As far as Oxford goes, the computational finance course is based in the mathematics department and so will be extremely mathematical and will realistically require a first degree in maths (or primarily in maths). They will probably assume fluency with abstract linear algebra and real analysis at the least. You can see that the course includes PDEs and stochastic calculus in the first term.
So look at the course structures for each undergrad degree you are considering and make a decision on that basis. I imagine either would be suitable at most universities but some universities offering "financial mathematics" may focus too much on statistics and applicable mathematics and not enough "core" pure mathematics.
However as above all that maths is way overkill and you will realistically never use it as an analyst in a bulge bracket bank. Most of what analysts do is just "advanced MS excel" and arguing about fonts. It's really not a mathematical field, if the mathematical side is what you are interested in you may want to angle for quant roles rather. Note that to become a quant would probably require a PhD, although that masters course and a PhD in a related form to it would be very relevant for that I think.