They probably just end up working together after a series of extremely brutal ambushes/counter ambushes. Neither side can really destroy the other, nor would either side particularly want to destroy the other. Aliens are functionally the same as random magical creatures, and random magical creatures are functionally the same as aliens for the MIB.
I should note that I am not arguing that potterverse will win. I am arguing about specific individual points like the mechanics of unplotable.
The main issue with potter-verse is that everyone is a moron.
While MiB is made up of hyper competent individuals.
Potterverse has the tools necessary to win easily. But those tools are wielded by simpletons and buffoons that will guarantee their loss
It's really not the case. Most of the 'wizards are idiots' complaints seem to be from the assumption that technology is somehow better, or that the people the wizards are chasing are just not going to use magic either. Wizards in Harry Potter objectively no more than we do. We think that 'love' is a biochemical process that happens in the brain, wizards have figured out that it is in fact some sort of extra biological process that happens in the soul. We think that faster than light travel is impossible, they perform it to get to work every day. The wizards in Harry Potter for all intents and purposes are effectively living in the Star Trek world but LARP'ing as 18th century cosplayers.
In regards to MIB being 'hypercompetent'. The first film they rely entirely on standard mid 2000's police investigation techniques such as 'check the morgue'. Their method of tracking the aliens requires a voluntary registration program; and even then only some of them are under active surveillance. In the 1st film, their 'runaway' is an alien that isn't allowed to set foot outside Manhatten, and they only caught onto him leaving once he was thirty miles away and trapped in traffic, which implies they're again relying on already existing infrastructure, such as government cameras. When cockroach man landed - In an exploding fireball - they penned him in 'Upstate New York' which isn't accurate at all. They then had to rely on murder reports and eyewitness accounts to try and track him. Even when the Arquillians were going to vaporise the planet, they still didn't have a real way to track the bug, they had to rely on guessing where he'd go. They only even knew about him in the first place because of a gossip rag.
In the second film, they have to move a giant carnivorous worm (Jeff) out of the Subway, and the only way they seem to be able to do this, is have an agent rodeo it and inject it with a tranq; rather than sending in some form of drone to do so. Then, Alien Dommmy Mommy managed to take out the entire MIB by flashing her - admittedly fantastic - tits and then wrapped everyone up in tentacles. They didn't see her coming, they didn't stop her; everyone just sort of ate shit and died. Nobody in MIB HQ seems to be armed, all their guns are in a lockup (Which makes sense really) once they're on site since all it took was a single disintergrator shot to end her - for a while - and at no time did any of the agents shoot at her.
A single wizard could literally teleport into the MIB HQ - or walk into it, they don't actually stop you from doing so in the films - and start blasting, or drop a mandrake and kill a bunch of people, or summon some fiendfyre. They have a security drone, it's 12 machine guns on wheels, which, while cool as fuck, seems to be extremely dumb. It empties it's entire bullet supply into an empty lift, then never shoots and again and is dispatched by a small grenade; any random wizard can blow apart stone fortifications, or shrink the drone to the size of a thimble, or just vanish it entirely if that's their primary defence.
In MIB3 they have seven moonbases; which oddly has the armoury stocked with Vector submachine guns. The moonbases are incredibly impressive. In theory spacetravel for wizards should be entirely trivial even if they don't try and teleport things since they can create reaction-less engines small enough to be carried in the hand, and easy enough to be sold like bicycles; we haven't seen any space travel from them, so there could be a bunch of reasons why ranging from 'They don't want to' to 'Magic doesn't work in space. The only mentions of space travel in the books are a wizard who claims he has gone to the moon, the space room in the ministry of magic which notes that space and time are the current 'limits' to magic (Which could mean hard limits, or simply the cutting edge of current magical research. It's not clear which.). Harry has to write an essay on Jupiters moon Europa and it's icy features and volcanic structure - they could have gotten that from the Galileo satellite that the muggles are using - and Harry at one point wants to buy a scale model of the galaxy in an enchanted crystal ball.
They have the Arcnet, but that was a gift from aliens, not something they home developed. There's time travel, but they only have two of them, and even then they don't really 'have them'. They're owned by someone else; and they don't want to use them.
I haven't seen the animated series so I can't comment on that. Also MIB3 is truly a dire film. In terms of peer to peer boom boom, MIB might have the edge; but both sides can instantly kill agents of the other with effectively any hit. In terms of mobility wizards are better since Agents cannot teleport at will. In terms of surveillance technology, both the Ministry and the MIB HQ seem open to anyone that can get into them, with fairly minimal defences. Wizards by their nature are always armed, and agents don't seem to be, but that would probably change very quickly. In terms of mindwiping; the MIB wipes a city. Wizards have on previous occasions wiped towns, and at one point they broke time so badly it started fucking with everyone's perception of days, hours, weeks. Which would have needed a planetary mind wipe, or a very good explanation real fast. Wizards could pretty easily get Agents under their control if they find them, and MIB due to OP fiat can see wizarding settlements as well. So as far as accessing each other, they seem pretty equal.
Going from what we see in the films, it's probably a case of very short, highly violent encounters where wizards find agents, track them for a bit, teleport in and blast them apart, or vice versa, where agents get word on wizards, rock up and light them up. Both sides can turtle up like crazy. Wizards can fuck off to the most remote inhospitable places on the planet with no way for the MIB to track or stop them, the MIB can fuck off to the moon, or space, or into bunker complexes they undoubtedly have. A lot of innocent aliens/wizards die in the process, eventually both sides reach a point where further escalation would end with massive loss of life/exposure, agree through clenched teeth to a NATO/Warsaw pact style agreement where each polices their own, and have a token 'embassy' from each side in their organisations. Would be a neat fanfic.
I assume the TV series has some insane shit in it, because cartoons.
