There are too many variables to be able to give you a blanket answer. In general, larger 30 caliber cans tend to be quieter than .223/5.56 cans due to the increase in internal volume (a lot of 30 caliber cans tend to be in the 7-10 inch range, while .223/5.56 cans tend to be in the 5-8 inch range). That said, apples-to-apples (7 inch 30 caliber can vs. 7 inch .223/5.56 can, of the same design/construction), the can with the bore closer to the projectile diameter will be quieter.
Check this test out. I didn't find it as applicable for me due to the use of bolt guns as opposed to AR-style weapons but it was a good starting point and nice comparison. Since they're a vendor and not an independent unbiased tester I don't take the data as gospel.
It isn’t easy to get 27 different rifle suppressors together for a test session. In fact, until the ATF made it faster for wholesalers and manufacturers to transfer silencers to dealers, such
My 300 WSM is quieter TO MY EARS than having it on either a 6.5 Creed AR or a 223 AR. Could just be the fact that it's an ar with noise coming out the side. On a 223 bolt gun it's about the same to me.
On a bolt gun all else being equal a tighter suppressor bore will net you better suppression. For example shooting 6mm Dasher through a TBAC Ultra 9 .30cal won't be as quiet as a TBAC Ultra 9 6mm would be.
BUT in a semi-auto the reverse is true to a point. In traditional baffle cans larger bores mean less back pressure which almost always means a quieter suppressor to the shooter (but not at the muzzle).
So the answer depends on your host firearm (bolt vs. semi) as much as anything else.
I get that people love to be sneaky and being able to have and use a can sounds so wonderful but am i the only person that loves going to see and hear and feel lout explosions like fire work displays our even louder gun fire at the range hell Id love to hear the live fire at the Aberdeen Proving Grounds growing up when they had them tanks and mini guns and howitzers and bomb blasts during the summer so why with all the make it quieter loud and proud ...never went to an nhra drag race and wondered if they could quiet the cars down so why the guns . Those people complaining about the noise are probably the same ones that voted for a socialist for president of what could be the country that was the united states ..
I get that people love to be sneaky and being able to have and use a can sounds so wonderful but am i the only person that loves going to see and hear and feel lout explosions like fire work displays our even louder gun fire at the range hell Id love to hear the live fire at the Aberdeen Proving Grounds growing up when they had them tanks and mini guns and howitzers and bomb blasts during the summer so why with all the make it quieter loud and proud ...never went to an nhra drag race and wondered if they could quiet the cars down so why the guns . Those people complaining about the noise are probably the same ones that voted for a socialist for president of what could be the country that was the united states ..