Basic Trope: Magic or other superhuman/paranormal power is overrated.
Straight: A perfectly ordinary rocket launcher blows up the 10,000 year old demon.
Exaggerated: A single company of muggle troops in the wrong place and time screw up a thousand-year conflict between entire wizard power blocs.
Downplayed: A wizard slaughters a company of muggle infantry only to get blown up by a cruise missile.
The rules of magic so go against conventional physics (Wild Magic, aversion of Magic A Is Magic A etc.) that the scientific method is as alien to the wizards as magic is to muggles. Systematic improvement of magic is thus impossible, limiting the ability of magic to advance.
Immortal Smug Supers sneered at muggles for centuries, not realising until it's too late just how far the muggles have advanced.
The Smug Super is very smug, and ignores the fact that, despite his power, he could still easily be killed by conventional means. Whereas before he only had swords to deal with, now he's facing guns.
Magic is slow, spells have subsonic travel time even after you waste time saying the incantation, can be dodged or blocked, and all defensive spells are reactionary while wizards have no Super Reflexes. This puts wizards at a huge disadvantage against muggles with firearms.
Magic always needs an organic in the loop. This makes mechanised industrial production like muggles have impossible, putting wizards at a logistical disadvantage.
Magic requires years of study and only so few people have enough magic potential to be useful in direct combat, whereas you can train almost anyone to use a gun in days.
Muggles are around present day in tech... Mages have a vibrant interstellar empire that makes The Culture look like cavemen.
Magic can do all kinds of things and at extents that leave Newton, Einstein and all other muggle physicists rolling in their graves.
Muggle technology looks superior until the mages pull out the really high-end powers.
Muggles win... only because wizard defectors tell on their own.
A third faction puts magic and technology together to form Magitek, which is superior to either individually.
Magic and muggle technology have their own strengths and weaknesses that the other cannot duplicate: technology gets the job done well enough and is available to anyone, making it the more economical choice. But its nuances are messy and unreliable compared to magic: stitches work at healing wounds, but healing magic is instant and painless. On the other hand, Magic is more effective, but only certain people can use it, making it far less available, and the people who can use need to train far longer.
Magic and muggle technology are about even; neither is substantially better or worse than the other.
Magic is always superior to anything muggles can do.
Lampshaded: "I thought magic would be stronger than this."
Exploited: A wizard challenges another wizard to a duel, only to pull out a colt and fill their opponent with lead.
Wizards keep researching and create spells that offer industrial efficiency so that they can keep up with or exceed muggles.
Wizards keep themselves informed of advancements in muggle technology and improve their spells to remain relevant eg. invisibility spells that also work on machines and guard against infrared or radar detection.
Deconstructed: Wizarding society becomes obsolete and is forced into hiding or destroyed.
Wizards decide to fight smart, not hard. If they can't outdo muggles in a straight fight, they'll just use guerilla warfare to avoid fair fights or esoterics such as mind control to set themselves up as The Man Behind the Man to muggle society.
Implied: In the drama Troper Magic, the focus is on a household that has both muggles and wizards in it. Although they don't fight, one side character has recently come back from war. The stories he tells imply that wizards held their own, but the muggles got a higher bodycount.
Plotted A Good Waste:
In a plot revolving around magic finally being returned to mankind after a Chosen One was fated to destroy the demon that required it be sealed in the first place. It turns out after the wizards tried hard to teach him magic he still hadn't learned. During the climax, rather than pulling out some unknown power that never was shown before, the Chosen One simply picks up a gun and mows the demon down, ending it.
The war shows that muggles and wizards actually have a lot to learn and gain from each other: Wizards learn to admire the low-hassle, mass-produced power of technology, while Muggles are highly impressed by the reality-breaking power of magic, and wonder if magic can be used to bolster their technology. After the war comes to an end, the Magitek industry explodes, bringing with it both new advantages and new issues.
Played For Laughs: Anything the wizard does is upped by muggles. To the point where, after he teleports for the first time, the news later shows that muggles have invented a teleporter by accident but they will be on the market in a week.
Played For Drama: The wizard is the only one who can truly renew nature after what muggles have done to it, but after being shown up over and over again he refuses to, claiming that, since everybody can clearly do better than he can, they should just do it themselves despite this being the one thing they can't do.