Master of Engineering vs Master of Science?

The main practical difference between the two degrees, as you point out, is the requirement of a research thesis for the MS degree. Generally, if you have aspirations of eventually getting a PhD, you should strongly consider the MS, as research experience or potential is a large factor in being admitted to a PhD program.

To answer your specific question, you should be a better researcher after completing an MS, and you will be better prepared for further graduate work. With an ME degree (considered a "terminal" degree), you'll simply have a Master's degree and (potentially) may have spent more time on your coursework. Whether or not this prepares you better for a position in industry is debatable -- as you say, many ME programs are one year, which may actually include fewer classes than an equivalent MS (although I've generally seen ME programs that have one or two more classes as a requirement than the equivalent MS degree).

As to which degree leads to more jobs in industry, I'd say it's probably about the same. Getting an MS will certainly not limit your competitiveness for industry jobs, while (as I already mentioned), an ME may limit your competitiveness for PhD programs.