This answer will assume the spell is being used in a game where attributes are either rolled and then assigned or purchased with a point-buy system. If the spell is used in a game where stats are rolled in order the spell is a little weaker on average, but the utility to a character with any given set of stats will be the same (the likely stat distribution changes, but what attributes each character with a given stat set will target and how good that probably is won't)
This spell should be 2nd level when used offensively
This spell, when used offensively, most penalizes a target reliant on Strength. No casting class you are considering (except the Eldritch Knight, I suppose) cares at all about their strength, so they can safely have as low as 3 in that stat. Kobold wizards can even have a Str score of 1!
The monster most possibly reliant on Strength is the Tarrasque. Replacing its strength score with a 1 changes its strength modifier from +10 to -5 and so reduces its damage by as much as 75 hp per round, unless the DM rules that the Tarrasque uses its constitution modifier rather than strength modifier for damage, but that would be mean. This damage reduction approximately halves the Tarrasque's damage output, which is somewhat better than giving the Tarrasque disadvantage on attack rolls like the otherwise superior second level spell Blindness/Deafness does, particularly since the debuff also stacks with disadvantage.
As a percent of damage, rather than an absolute value, some other monsters are worse effected. The Ogre is the worst I can find so far, with its average damage dropping from 13 to a little over 4-- a 68% reduction.
This is the best the spell can ever be offensively, and it's not reliably better than a similar second-level spell, excepting only its ability to stack with other effects unlike disadvantage/grants advantage debuffs. Considering the spell requires Concentration, that's a hard sell.
The spell is completely absurd when used defensively, changing the nature of the game beyond the effects of any other spell besides possibly Wish
The spell also gives you the score you steal, temporarily. That is okay when the stolen score is an enemy's, but ridiculous when it is used in conjunction with an ally. Let's say my Wizard casts Swap on something with more Int than I have. Then my allied Cleric casts Swap on me. Now I have my ally's Intelligence and he has the monster's. I end my spell and give the monster my ally's Intelligence, then my ally ends his spell and gives me the monster's while I give him mine. Now the monster has my Cleric's dump stat Intelligence permanently, and I forevermore have whatever absurd Int I managed to find on a monster.
Alternatively, let's say I have a Potion of Hill Giant Strength. I quaff said potion, then cast swap on an allied fighter or some such. Now both our scores are 21: mine because I'm still affected by the potion and his because my score was 21 when we swapped. Eventually, the potion wears off. My score drops to whatever my number normally is, but his doesn't-- he was never affected by the potion. Then the spell ends and I go off with a permanent increase to my strength score. If I instead end the Swap spell first, the fighter is the one that gets the permanent increase. This only gets worse if rather than a potion I am possessed of a belt or other permanent increase!
While 5e has a lot fewer ways to increase ability scores temporarily than 3.5 did, and also implements hard-caps on ability scores if one plays with twitter erratas, this sort of Manipulate-Form-esque permanent ability score raising combo is still ridiculously powerful. Being able to alter temporary increases into permanent upgrades is a problem unless your players are already going around with 30s in the stats they care about.
This spell also is ridiculously useful to necromancers
Necromancers can only control permanently undead with a low-enough intelligence score. By having an allied Mummy Lord or similar swap intelligence with me after swapping intelligence myself with a high-int undead monster, I can save myself a lot of the trouble that normally comes with enslaving powerful undead beings.