<p>In terms of material engineering, <em>materials</em> themselves are pretty versatile, as in, you use materials in pretty much everything. As in chemical engineering, it’s a niche that shows up in lots of industries.</p>
<p>I still think, though, that mechanical and electrical engineering, if you were to study both of them, you’d not only have the overall engineering mindset (great for deductive work), but you’d also probably be able to figure out how pretty much anything works, and talk at great length about it.</p>
<p>So, it kind of depends upon what sort of versatility you mean. Do you want to understand everything, or do you want to have a breadth of fields available for you to work in?</p>
<p>By the by, I really don’t think that industrial engineering that versatile as an engineering degree. It’s particularly about eliminating wasted money, time, and energy… It’s pretty specific, and can only really be applied to, surprise surprise, industrial applications, in comparison to EE and ME.</p>