been to both recently...Absolutely no safety concerns...Well perhaps the south side of Pest (around the Ramada hotel) is a bit shabby but I'd say in a non-threatening way.
Just one small caveat emptor: NEVER pick a taxi up in the street. Even if it's nothing dodgy with an overcharging driver, all taxis in every CEE country I've been in are significantly cheaper if called over the phone....
Taxi companies I've been satisfied with:
PRG: Profi taxi 844 700800
BUD: Citytaxi 211 1111 (not 100% sure but this must be the one)