i was wondering the same thing a while ago, the difference between maya's hair system and texture hair is the render time.....maya hair will give you a realistic look, but you have to consider things like applying dynamics so the hairs falls into place and doesn't stay straight in the air like you used hair gel on it, you have to make sure the hair doesn't go through your model's head, it will also take a longer time to render.....while texture hair if you do it right, will give you a fairly realistic look with less effort and less render time because all you will be rendering is a plane with a hair texture on it instead of every hair particles from the maya's hair system.

i never was able to find a texture hair tutorial for maya online, so i just went ahead and did the way i knew, came up with this result.
first i made this in photoshop:


then i tested it in maya by applying it to plane then i put the plane next to a sphere:


not the best looking hair i know lol, but i did that a while ago and i'm still learning till date. :p


P-S: hey this might be a tutorial idea for SM lol, someone who's an expert in this could show us how to make textured hair