My experience (USA):
MS = Master's work with thesis & defense
MEng = Master's work without thesis, but final project with defense. My ME was a lot broader education than my colleagues getting their MS, even though we did essentially the same work. I survived grad school thinking MS candidates were being trained to be applied mathematicians, I was getting advanced practical training in a broad assortment of engineering subjects.
Out in the workforce (cynical view): most managers and HR folks don't have any idea what is involved in getting, much less have any idea of the value of obtaining, an engineering degree of any sort. To the non-schooled majority of hiring decision makers, MS = ME = BS(4yr) = BS(2yr) = AS(2yr) = Talented Floor Sweeper. The degree is important when you are getting a job. After you've got it, you are at the mercy of the unschooled.
After gathering all the ideas and opinions here, get what suits you.
TygerDawg