I suggest you read this book, called the Union of Dzogchen and Boddhicitta by Anyen Rinpoche.
Basically, like water has several qualities, wet, fluid, clear... yet still it is water... the deep mind of reality has similar. Boddhicitta is a quality of this deep mind. It is related to the Middle Dantien - the Heart - often referred to simply as compassion - but as stated above it is more than just compassion in the ordinary sense and related very much to the Boddhisatva vow.
The book clearly explains why it is not enough on its own to attain true enlightenment. It also says the same about Dzogchen alone, which is related to the upper Dantien and the Clear View. It is only through a synthesis of both Dzogchen - right view - and Boddhicitta - compassion brought about through the right view - that according to Tibetan schools you gain true awakening to the natural state.
I would also suggest that it is just as important to focus on the Lower Dantien and keep rooted on the ground in this, that way keeping the true connection with all qualities of reality related both to the Dantiens and the microcosmic Heaven/Earth principle in man.
Hope this helps...