In the mindset of the every student, there exists a very bold aspiration, to pursue masters in the international universities. However, every student doesn't have a clear understanding between M.Sc. and M.Eng. While I have a little knowledge about how this influences in other streams of engineering but I can assure it matters a lot in mining stream.
You can think what's a big deal if a student applies for M.Eng. or M.Sc. as they both represent the masters degree. The master's degree you choose has a totally different influence in your career and on your mindset. Then what is the difference between them??
By definition:
Master of Engineering (M.Eng.) can be either an academic and professional master's degree in the field of engineering.
Master of Science (M.S. or M.Sc.) is granted for studies in engineering focused on the growth and improvement of the subject.
The students are not fond of definitions which make them more confused towards these things. Let me help you to describe a little more about these in a non professional way.
Master of Engineering is a degree for those who are interested to increase their knowledge in technical aspects of the subject and will be joining the industry after their graduation. In this program, the time of graduation can go from one and half year to that of two years depends on completion of the technical courses. In some universities, there is a clause to completion of program which include to present a technical paper. While in some other universities, student should undertake internship and present a technical report about the internship for graduation. This program is totally oriented towards preparing a graduate towards a professional career path i.e. towards an industry. 
Master of Science is a degree for those who are interested in research. Research means performing experiments to develop something new such that it helps the industry in one form or the other. In this program, you will be allocated a project to develop the experiments and perform it under the guidance of a professor and complete a thesis on the performed experiments and findings. The time frame of the graduation depends on the completion of the thesis which may take up to two to three years. Especially, this program is for those who are interested in pursuing Doctor of Philosophy (PhD) while the M.Eng. students cannot pursue PhD. The career options for this program can lead to industrial jobs especially in Research and Development (R&D) sector of the industry / Scientist / Professor.
Opting a degree, can make you focus towards your future aspirations. Both the degrees are focused towards the professional career path in their respective manner, now it depends on the students whether they want to pursue masters by research i.e. M.Sc. or M.Eng. which is professional masters degree.
There is a saying "No pain No gain". The real deal in the M.Sc. program is to find something new and presenting the findings in the form of publications and to find the right career forward. While that in M.Eng. program is to create a network inside the industries to obtain a position in the industry.
Hoping the prospective students will choose their degree wisely and wishing the students all the very best for their future.
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