I'm glad you raised this. 

* Neuroscience is the term that I hear more people use. 
* Google returns 10 million results for neuroscience and and 2 million for neurobiology.
* Neuroscience sounds closer to cognitive science to me; whereas neurobiology suggests a closer proximity to biology to me.


If others agree by either upvoting this answer or offerring supporting comments, or other supporting answers, we could:

* edit a few of the neurobiology tags to neuroscience
* create a tag synonym between the two terms