It's naive to lump all forms of engineering together and claim they aren't as good. That being said, I did my undergrad in engineering and I think industrial engineering is one of the weakest engineering disciplines you could come from if you want to pursue MFE. Biomedical, chemical, and some forms of electrical too.
However, disciplines like control systems, heat transfer, fluid dynamics, structural dynamics, and signal processing will prepare you really well. It's not so much the degree as the type of tools you use. For example, your degree could be EE but if you're using search algorithms or doing a lot of signal processing in the frequency domain then you're going to be better off than a pure mathematician or a programmer. Engineering is great for developing the mindset that will help you succeed in FE. Different systems, similar tools, same thought processes.