Hi Shanti,
Both types of grass are of the same family. But interestingly, they behave differently to sunlight.
Link for Manila Grass
http://www.desert-tropicals.com/Plan..._matrella.html
What I like about it :
Slow rate of growth - don't have to cut so many times.
When in full sunlight, they don't grow tall. (I plant this in my garden since 2006, and up till today, i've never mowed the lawn, as they remain as short as 2cm tall. Very nice to step on.
But in the shade, they can grow quite "tall".
If you have plants in your garden planted in the ground, do make sure that both types of grass does not "choke" the plant, as they compete for food and water. Therefore, it is important that you trim and leave at least a foot's space between these grasses and your plant for management. By "management", I mean, you can trim the grass as they creep into the defined space between your grass and plant.
Taiwan grass - lots of link from google.
Fast growing - pay more for gardener to trim.
Even in the sun, they can grow quite long, quite fast and creates a fluffy bundle on the ground. Sometimes, because of the "thick" and uneven bundles, you then need to mow the lawn to make your lawn look "even". (with Manila grass, this does not happen).
So, I'd say that depending on where you want to plant (sun or no sun spot), and whether you prefer thick grass or thin layer of grass; or even proximity to plants, or you plan to plant taiwan grass to semi-cover tiles-on-ground or railway sleepers, then you need to choose the right grass.
u can learn more about your grasses, if you go
www.allaboutlawns.com.
Good luck.