In general, the faster the speed the greater the frequency response, the less wow and flutter and the greater the dynamic range. The exception here is video systems (also used in DATs) where though the tape speed is relatively slow, the recording/playback heads rotate, effectively creating a higher tape speed.

Also a minimum of 7.5 inches per second is required to physically cut or edit the tape. 

Cassettes run at 1.875 inches per second (4.75 cm/second) while some 4 track cassette devices (“portastudios”) run at 3.75 i/s (9.5 cm/s). 

Reel to reel tape runs at 7.5 i/s (or 19 cm/s) and 15 i/s (38 cm/s)- the latter being the professional standard.  Occasionally one may find analogue machines set to run at 30 i/s (76 cm/s).