One difference is that the Vatican requires a very much longer waiting time before submission and final declaration. Arguments Against the Prizes Large prizes for notoriously difficult problems encourage a romantic view of a mathematical career. Of course, the world must always have its Shackletons, Lindbergs, and Hilarys. But it should be recognized that obsessive devotion to a single problem can destroy a professional career. An example, based on the experience of a real-life mathematician, can be found in mathematician and film maker Apostolos Doxiadis's novel Uncle Petros and Goldbach's Conjecture.
Large prizes feed right into the star system, which is now endemic and getting worse.
They emphasize the individuals and not the accomplishments as such. Large prizes underline commercial values. Theorems can become commodities. The heros they bring forth will be one part Tiger Woods and one part Sammy Glick. The Fermat problem was solved only recently, almost a century after the announcement of Wolfskehl's prize.