In the same situation as you OP, I have an offer from a great uni in Neuroscience and from my research, the prospects are that there are jobs out there! It is all about how you sell yourself to the employer over anything else. Knowing what they are looking for and how you have fulfilled this requirement and being able to talk about it, this is why employers want experienced people so they don't have to explain things over and over.
However, neuroscience is a sector that has seen lots of cuts due to the lack of progress in the past years, despite large investments from pharma companies. This has meant there are fewer jobs but the problems remain, a case of low-hanging fruit being picked. So over time, there will be an increased demand for employment due to the strain that neurological disorders put on the NHS etc.
But there has been promise in the area with, I think it was, Eli-Lilly producing the first alzheimer's therapy to reach Phase III in 27 odd years. But the industry faces lots of issues, like the patent cliff and me-too/biosimilars which are forcing it to become more moral or strategic depending on your cynicism..
So on the whole I, though biased, think doing an MSc in Neuroscience is fine, you will find work and have lots of transferable skills; most consider it a stepping stone to PhD more than a final qualification. Though if you do a grad scheme afterwards you should be ok with employment if you don't want to do another postgrad qualification.