I was born in Nijmegen (at the university hospital "st.Radboud"), but I've never lived there, it's a fun place though. Nijmegen University is mostly known for it's Medical academy and socio/political studies, are you doing either one of those?
Amsterdam is on different scale...as in 1milion vs 200.000 people, Nijmegen just celebrated 2000 years for the city of Nijmegen (Noviomagum was founded by Roman Legion X "Gemini" with a Batavian city right next to it "Batavodurum") and is very un-dutch, due to the hills of the area. Amsterdam is the prototype dutch city, canals, etc. but Amsterdam is also more cosmopolitan and has two universities.
Difficult compare, even harder to say which is better...if the stuff outside of studying is of importance, Nijmegen is pretty selfcontained, Germany is very close, but no major cities on that side. Dutch rail is well organized (even if we complain) but the nighttrains can get you from Amsterdam to the entire "randstad" (amsterdam,leiden,the hague,delft,rotterdam,utrecht) even in the middle of the night. Due to the size of amsterdam, you may never get around to checking out other places
The people are also very different from place to place. In US terms: Amsterdam think NYC (aka New Amsterdam lol) Nijmegen= way more laid back. you certainly won't be in Kansas anymore.
I agree with Joe^2, depending on your subject you may also want to check out Leiden (law, bio), Groningen (physics) Rotterdam (business, econometrics) Utrecht (history, languages) Maastricht (international law) or the technical university at Delft (aerospace, architecture) and the life sciences at Wageningen...no university in the Hague (@pawel)
...but there are more elsewhere