In all the books I have read (ok, that makes it sound like huge numbers... but it is a good handful!), neons are difficult to keep. They also come with their own personal disease that doesn't affect other tetras (neon tetra disease, obviously!).
My first five neons died rather quickly, howevr I did put it down to the fish shop they came from... never was impressed with it (though in retrospect, it was a fairly new tank, only a month or so old... so I could easily have been falsely accusing...). I got five more neons after my glowlights had been happily swimming around for several weeks. I still have four neons, one mysteriously disappeared (I mean, completely disappeared, no body or anything! Another unique feature of neons...).
Cardinals are apparently a lot hardier (and some people reckon prettier!). Certainly my sister has cardinals, and I don't think she has lost one. She got them after I advised against the neons based on my experience!
Neons are great, but, nothing beats clown loaches in my book for great fish...