Yes, there was co-existence. It is almost always the case that the new species evolves and interacts with the old before some solid advantage emerges, or some environmental change occurs, that puts the new species to the fore and reduces the old species, perhaps to the point of extinction. This is true not only for the development of human species, but for the development of all species.
Quite simply, two or more different species must exist together in the same ecosystem for a period of time before one demonstrates that it is more fit than the other. Initially, these are likely to be sub-species, with some interbreeding.
The latest genetic evidence is that current human beings have both neanderthal and cro-magnon ancestry. There are various theories. My favorite is cro-magnon female ancestry (as shown by the mitochondrial DNA) and a mix of cro-magnon and neanderthal male ancestry.