EGPWS has advanced features of a terrain database enabling a look-ahead function, a terrain-floor feature, and airfield/runway recognition; there are also many software mods to the original warning system which maintains the very high reliability of the alerting system.
The first EGPWS's used the best available high-accuracy navigation input; those aircraft with DME/DME or IRS (or GPS failure) could suffer a map slip – the conditions of susceptibility and/or geographic location were alerted in the AFMs; this also included issues of QFE.
In more recent aircraft, EGPWS nav input can be from a range of external sensors – GPS being the most accurate, but the EGPWS also has an optional (the better overall option) internal GPS which helps avoid any external nav errors, but this option can still use any external input for comparison.
Later modifications have added Geometric Altitude, only available with GPS; other options included peaks mode and obstacle database – an invaluable tool if updated regularly (it was free).
AFAIR the early A320s were equipped with the Honeywell EGPWS, but later aircraft may have the T2CAS (TAWS) from a different vendor. There are differences between eash systems' inputs and with computation, but both meet the same operational requirements spec.