This is going to be a bit disjointed, but my mind doesn't always go from Point A to B in a straight line. Still, I'm at least going to answer the original question a bit.
As a fan of a certain type of show, I have seen similarities but nothing comes all that close. This is all very close to the sentai genre. My first thought was Mystic Knights of Tir Na Nog, though it wasn't quite so complete an outfit. Just a group of people who use magic to turn into superpowered knights and fight the forces of evil.
I also thought of Power Rangers Mystic Force, where magic-based power rangers turn into their giant zords. Of course, the size is bigger and it's not the same as just being inside them, but I felt it was closer than the traditional "piloting giant mecha in a cockpit" type of thing. On top of that, a couple of the characters are magical knights who are bigger transformed.
As a special mention about the idea Rincewind had of Stone Age Knights, that would make it more similar to the Japanese sentai Ky?ry? Sentai Zyuranger, which was adapted to the United States as Mighty Morphin' Power Rangers. In Japan, those magical suits and Zords were created back in caveman times to be used by ancient warriors fighting an evil sorceress, using animals from back in then. You know, the Stone Age when humans lived alongside dinosaurs.
Lastly among the sentai, there's Big Bad Beetle Borgs, where a genie magically gives a group of kids the ability to use adult-sized armor to fight monsters.
Then there are the non-sentai similarities, though those tend to not have magic, like your Warhammer 40k and Starcraft Space Marines, or Battletech's Elementals. https://www.youtube.com/watch?v=ub1uDOqX4I8
On top of that, we have comic books to think about. Lex Luthor's power armor, the bigger Iron Man armors, Jim Gordan's Batman power armor, and the Destroyer Armor all come to mind. In the Destroyer's case, it's magically-created armor that is inhabited by the soul of the user, not the body. Even Guyver might kinda count, though there's a big difference between the films and manga.
Finally, as others have pointed out, pretty much any giant mecha series is going to be at least a little similar. Gundam, Gundam Wing, Mobile Fighter G Gundam, Zoids, Toppa Gurren Lagann, Vandread, and particularly Tekkaman Blade. That one's where a guy has the ability to transform into a larger, armored form to fight aliens alongside a group called the Space Knights who fight using giant robots. In that case, it's aliens using crystals, so not magic.
So in my limited knowledge, the same broad-strokes stuff has been done, but I can't think of the absolutely exact thing off the top of my head. That said, I don't know as much about anime and manga, and that's might top guess for where you'd find something almost exactly the same if it exists.