Nope

All will shoot slugs just fine, it will really come down to the rifle and the tune you have. The effectiveness of the slugs will depend on what you are shooting them at. If shooting at paper then it wont really matter..... if shooting at something like a deer you don't want to go with a 177.
 
I was told once that you can only make a projectile go so fast because of the volume of air. A 30 cal has more volume than a 22 and that's why you can't get more speed on a .22 so it just depends on how much energy you want to have hit so if you want a big bang go for 30. If you want a smaller but more precise bang go for 22 because of the wind resistance, the 30 is going to hold back more wind than a 22 but the 30 is going to hit harder. Since we can only cram so much air energy behind that projectile it's not like a firearm where we can stuff a whole bunch of gunpowder behind a projectile and make it go really fast. We are limited because air can only be squeezed so much so we can only get so much energy because we're limited by the volume.
 
When using slugs you're ahead of the game with faster twist barrels for mediums and heavies for higher bc's.

The more energy you want on arrival tends to favor larger calibers. There is also more sight picture upset. More air is required. Can cost more. Sometimes higher BC, and these hit hard.

My AGT Vulcan 3 was a great choice for 60gr Altaros Queens. Had it tuned by Derrick Wall and GTG ever since. Very dependable and precise. I think it's a 17 twist.
99 fpe.

The 22 cal Skout EVO is also great with 32.3 grain Altaros Smooth. This is a 15.75 twist. 49 fpe.

Huge difference of energy transfer as well.

But the EVO is more forgiving to shoot and 30 rounds on tap, plus higher shot count per fill, just makes it a more fun experience.

I can still hit smaller steel at 250y fairly easy with the EVO though it's not moving the steel much.

Just all around I enjoy the EVO more but the V3 excels the farther the distance increases.

The EVO is easier, or shall I say, more convenient to tune. Even I can tune it and 22 cal with slugs has worked out very really well.

I haven't tried Altaros 40gr King's in the 900's yet which will bridge the gap between those two guns and power levels.
Could even try the 56gr but it'll be single loading only like how I do with the V3 because I haven't modified a magazine for these long slugs.
 
I LOVE my .25 & .30 guns. I don't shoot paper & my .30 is my favorite & my go-to gun. That being said, I've recently come into possession of a .22 slug gun (Edgun R3 long - gotta love those eastern European guns!) & it is absolutely amazing both in accuracy & power. 150 yards & farther is no problem for the Eddy! The SMACK of the slugs hitting a squirrel is almost as loud as a .22 powder burner (gun itself is QUIET). It could definitely be tuned down but I'm not concerned about the sound. Pretty sure you'd be happy with a .22 that's both pellet & slug capable. And, as said before, the ammo options are wide & varied in .22.