(Oddly enough, my childhood intuition about equals signs isn’t historically accurate—the equality is actually supposed to be represented by the equal length of the two strokes.)
It took me a long time to differentiate the symbols because, before using the alligator metaphor, my teacher tried this one: cross a line that goes perperdicular to the bottom part of the symbol. If it turns into a 4 it's smaller than; otherwise, if it turns into a 7, then it's bigger than.
I remember seeing a "5 < 8" and thinking "ok, I know which number is smaller and which one is bigger, and I know how which symbol is named, but which one should I use?" For some reason it wasn't obvious to me that I should read the assertion from left to right. I just saw two numbers and I didn't know if I should indicate that one of them was bigger or that another was smaller—both assertions were true. I remember having a list of exercises to do as homework and just circling the bigger numbers in frustration.
When I hearded the alligator metaphor, however, I got it instantly.
Just like how I was taught the difference between "<" and ">". Our teacher drew the rest of Pac-Man around the "<" or ">" so that we'd think of "<" or ">" like the mouth of Pac-Man. It wants to eat the larger number. But that was back around 1983 when Pac-Man was all the rage (when I was drawing Pac-Man eating ghosts on my folders).