If I understand you question properly, you're thinking of going with a 223 suppressor to use on your rimfires, yes/no??
I have a couple TBAC rimfire cans (22S-1, 22L-1) and a 223P-2. I've used my 223 suppressor on my rimfire guns and I couldn't tell any difference in sound reduction between them. Maybe a meter could pick it up but to my ears I couldn't tell one from the other.
The biggest thing you're going to notice is price and weight. My rimfire cans are a lot lighter than my 223 can and they cost half as much. Also, nearly all rimfire suppressors can be taken apart for cleaning, to some, that's important, to me it wasn't which is why I have sealed rimfire cans.
If you are trying to have one suppressor that will cover your rimfire needs and your .22cal centerfire needs, obviously you'll have to purchase a 223 type can. They will work fine on your rimfires but, depending on how many 22 rimfire rounds you shoot through it, you may need to have it cleaned every so often.
There are many great 22 cal centerfire cans on the market so you'll have plenty to choose from but depending on what 22 cal centerfire you'll be using it on, make sure what ever you buy is rated for what you'll be putting it on. If all you shoot is a 223 you'll be good but if you have one of the hot rod 22 wildcats and the barrel is on the shorter side, it's possible it may not be rated for that so always ask before you buy.
Remember, when in doubt, BUY BOTH!