Niether Y-up nor Z-up is mathematically wrong, but the Z-up is more generally used. The y-up cartesian system is used widely amongst animators/3D artists, due to the natural transition of evolving from the 2D X/Y to include moving away from the camera - which is Z (as in Z depth). The Z-up system is used mainly by designers and 2D people , who prefer to keep the X/Y on the plane (as this is how their drawings will lie).

Maya uses the Y-up system as default, but it can be changed to Z-up if desired.