A M Eng is 8 grad courses and a paper. A M A Sc is 4 courses, a real research project, and a thesis.
In my estimation, the M Eng likely teaches you very little that is useful, given that it's tough to find eight grad courses at a typical uni that are taught well enough to be truly worth taking. The M Eng is a popular option with people whose employers are paying them to obtain a Master's degree, because all you need to do is attend lectures, do some assignments and write some exams- and over the longer timescale of part-time studies, you are more likely to find eight worthwhile courses over several years than you are in a year or two, since many are not offered every year.
The M A Sc has a hope of teaching you something useful, by getting you to actually study something in depth, on your own- possibly even requiring you to build some apparatus and make some measurements, and then to try to analyze and understand what you've observed, and communicate that with enough rigour to withstand review.
Employers that know this difference value it accordingly, which in my experience is still very little. Most give you perhaps 1 year of extra "experience credit" for a Master's degree. Employers that don't know this difference don't give you much credit for your Masters' degree at all. Again, your mileage may differ.