Mindfulness and self awareness are two similar but distinct capabilities. Mindfulness is observing one's internal state without judgement whereas self awareness is the ability to recognize your feelings, differentiate between them, know why you are feeling these feelings, and recognize the impact your feelings have on others around you. So self awareness is seeing the discovery of mindfulness.
One of the self awareness practices I tried was journaling. It was a new experience for me but was really fascinating to see what sort of thoughts would flow onto paper. Perhaps it's just that it identifies trains of thought and allows it to be explored more thouroughly then a fleeting synapse firing.