<p>One example comes to mind, although I don’t know how good it is. I’d generally consider game theory to be “harder” than differential equations, and economists do game theory whereas engineers do differential equations. This is academic, though, in the sense that you can do a very cursory treatment of game theory in an economics program and a very rigorous treatment of differential equations in an engineering program, and vice versa.</p>
<p>I would offer, though, that the “hardest” part of both economics and engineering programs is the mathematical component, though, and as such, the difficulty (real or artificial) of the programs - which can be inferred from graduation/retention rates - should correlate fairly well with how rigorously the programs do the mathematics. In other words, see which programs have higher drop-out rates, and maybe even see whether you have more economics -> engineering or engineering -> economics (normalized for the sake of comparison) transfers.</p>
<p>Also, the difficulty of the mathematics involved will very across engineering disciplines, somewhat at least. The variation is greater if you count software engineering & computer science as “engineering”, in which case, I’d be of the opinion that these involve the hardest mathematics… surpassed only by mathematics or rigorous statistics degree programs. Of course, as a math guy working in software, you might take this with a grain of salt.</p>