Alphanumeric (character) LCD module vs Graphic LCD Module

Comparing Font :

A large number of alphanumeric LCD modules are based on the Hitachi HD44780 which contains a character generator.
All the Character LCD controllers have their own fixed font and character generator. (CGROM)

Many of the newer Graphic LCD controllers have their own internal font. So you can send it as text, and it will draw it for you.
(For example the good old T6963C is having an internal CGROM) Others do not, in which case you will need to send a bitmap of the character to the display.
The size of the library code that drives the actual device is obviously larger for the Graphics chip, and an external font uses program memory.
If you are tight for memory space then choose the type with an internal font and smallest library.