Although the Fields Medal somewhat corresponds with the Nobel in terms of prestige within its community, I don't think it's really all that similar. Since it's only offered to mathematicians under 40, the philosophy is quite different - being over 40 is not a detriment to mathematical research skill, so the Fields isn't necessarily awarded to the creator of the best research. Also, I think that the fact that it is only awarded every four years is a bit self-deprecatory, as it seems to imply that mathematics research is progressing a few times slower than physics or chemistry research (which I disagree with), and because of the age limit I imagine the award creates a lot of stress for people who are almost 40. I know the conditions of the award were determined by the benefactor, but I don't like them.
Personally I feel like the Abel Prize is a more direct comparison, as the prize money is much closer to the Nobel (about $900 thousand USD, compared to the Fields Medal's ~$15 thousand) and as, like the Nobel, it has no age limit and is awarded anually.