Both are correct, but they are used in different contexts.
1) Me falta: Can be used in two different constructions.
a) It is used when you are referring to part of a process or thing.
Me falta dinero = I have some money, but not the whole amount I need.
Me falta leer dos capítulos más = I have read most of the book, I just have to read two more chapters to finish.
Me falta limpiar la cocina = I have cleaned most of the house, I just have to clean the kitchen and I will be ready.
b) It can also be used to express the need of something, same meaning as "me hace falta".
2) Me hace falta: It is used to speak about something you need.
Me hace falta leer más = I do not read enough, I should read more.
Me hace falta entender este concepto = If I do not understand this concept I will not be able to advance.
As you can see in the last two examples, there is process being performed, the person is just expressing the need of "reading" in the first case and "understanding" in the second.
Also, after "faltar" or "hacer falta" there are no verbs, these are gerunds (id est, verbs that are used as nouns).