It has not ever “been established” that Loki’s magic is “mostly illusion-based with shortcomings.”
Loki is, in fact, “the most powerful sorcerer on Asgard,” according to Kevin Feige.
This is a short list of what we know for sure, from the films, that Loki can do—we don’t know what else he is capable of. (I expect we will see other powers emerge in the new Loki series.)
Ice powers (he’s a Frost Giant).
(Feel free to watch Thor, The Avengers, Thor: The Dark World, and evening Ragnarok to find where Loki uses all of there powers. If you can’t find them all, let me know and I’ll post the gifs.)
Or, just check out Marvel’s official bio for Loki. They give a nice list of Loki’s powers, but it doesn’t include everything we’ve actually seen in the films.
But that’s not all. Loki has superhuman strength speed, agility, durability, healing, and longevity, which Dr. Strange does not have.
Because of these powers, Loki has survived all of the following and more:
Being shot with automatic weapons.
Falling through space and wormholes (at least three times).
Getting blasted point-blank with a SHIELD super-weapon.
Being stabbed through the chest with a huge sword.
Any of the above attacks would kill a human instantly. Dr. Strange would need at least a few seconds to work a spell, or do that thing with his ring, or use the Eye of Whatever stone to survive any of those attacks. So, he’d die—unless his cloak-friend managed to act quickly enough to save him. (I don’t think having a magic cloak buddy should count as one of Dr. Strange’s powers. Unless we want to count Loki’s accessories as well—starting with the Tesseract?)
Now, I’m not taking anything away from Dr. Strange. He is the Sorcerer Supreme, and undoubtedly the strongest sorcerer on Earth. But Earth is not Asgard, where magic is an everyday thing. Which reminds me of a few more relevant points:
Loki is a genius, tactician, strategist and “always 10 steps ahead of everyone else.” He has studied combat and fought in countless wars. Dr. Strange is also a genius—but his learning is primarily in medical science.
Loki has lived for over 1,000 years and has studied magic since he was a child.
Loki can hold Infinity Stones in his bare hands without burning up. Humans can’t do that.
According to Thor, Loki knows secret paths between worlds that no one else knows about. Only Loki doesn’t need the Bifrost.
Loki has his own “dimensional pocket” where he can keep pretty much anything he wants apparently, including the Tesseract.
In the first Avengers movie, it took all of the OG Avengers (plus Fury, SHIELD, etc.) to stop Loki. As you may recall, there would be no Avengers if not for Loki.
Loki has held his own in extended battles with Thor 1:1 twice. In fact, overall, Loki is generally considered to be as powerful as, or more powerful than Thor.
Now consider this. How did Dr. Strange get his magic? (Aside from being given that ring thingy, the Eye of Whatever, and the Cloak-buddy, I mean.) He studied. He practiced. He read the spell books. He worked hard at it.
So did Loki. Just about 1,000 times longer than Strange.
One more thing: Dr. Strange is a human. Loki is a god.
Okay, now that we’ve cleared that up, I’ll just mention that I really don’t blame you for thinking Loki can only do illusions. Inexplicably, Loki didn’t use most of his powers in the last three films—not even to save his neck in IW. Thus, the filmmakers of Ragnarok and Infinity War severely underpowered him.
And THAT is precisely why “people cry bad writing” with regard to Dr. Strange supposedly overpowering Loki.
I thank you for your time.