Ok, so I was wondering whether Stanford or UCLA would be better for a major in applied mathematics. Ideally, later down the road I would like to attend a prestigious MBA program at another top school. I have managed to accumulate 114 AP credits, making UCLA pretty appealing, but I do know that Stanford is pretty prestigious. Would a degree from Stanford be worth it in the long run? Quality of life is not an issue, I absolutely love both campuses and their locations.
Um, I think you should apply to both and see if you would even get into Stanford. There is no point in imagining what selective school you should go to.
First see where you get in and what you can afford. If both are still options, visit both campuses to see if one feels like a better fit.
Starting in 2017, Stanford will print their diplomas in AR HERMANN. You can’t hang that on your wall. 
This is a good question and perhaps you can come back in the future and let us know what you decided and, on reflection, if that was the right decision. I recently visited both Stanford and UCLA with a view to studying maths. Some reflections. Stanford appears far more prestigious. You can feel it and see it. The initial research I’ve done suggests that Stanford students may earn more on graduation, be more desirable by Ivy League post grad universities (like Harvard) and generally you would have a more connected prestige peer group that you graduate with. But if that’s not your personality/lifestyle going in, it could be hard to socially enjoy. UCLA feels more accomodating of different personalities and feels more relaxed. And UCLA can’t be that bad in maths - imagine having Terence Tao as your mentor. I recently also read a couple of interesting reflections on www.Jetsmathblog.com on the two universities. Ultimately, there may be no universally perfect answer and it may be personal - does “worth it” mean “earn more money” or “be assured to get into an IVY League postgrad” or “soul fullfilment? etc”
Stanford receives 25 applications for every spot in its freshman class. Explore all your options and build a deep list of schools in your desired major. Both great schools.
Have fun your senior year.
Cross that bridge . . .
It’s hard to imagine turning down Stanford though.