Use the correct size for proper cleaning.
But, having experience in the following area...
(...) using a 45acp bronze brush to clean a 44cal bbl and/or cylinder?(...)
...I feel obligated to comment.
Most companies don't actually make .44 caliber bore brushes. What they actually make are ".44 caliber" bore brushes.
Don't understand the difference? Don't feel bad, most people have no idea.
Most gun cleaning companies don't make .44 caliber bore brushes, because they think the average idiot customer ... errr, ehemmm, gun owner ... will be just fine sticking a .45 caliber brush down the bore.
So, most ".44 caliber" bore brushes are exactly the same as the company's .45 caliber brushes. A few companies even say right on the packaging that it's a ".44/.45 caliber" brush, but most don't.
In over 15 years of trying to find TRUE .44 caliber bore brushes, I have only recently found (of all things) Brownell's .44 caliber
nylon, pistol bore brushes to be of proper size. All other ".44 caliber" bore brushes are actually re-labeled or co-labeled (.44/.45) .45 caliber brushes, including the bronze, pistol Brownell's bore brushes.
Who actually makes them, I have no idea. But they're the only true .44 caliber brush I've ever found.