Thread chasers generally don't cut, they more squish or roll or try to push the damaged threads back into place and scrape off some crud and rust, they may cut but usually not well or much. Not ever intended to cut threads from scratch.
A tap or die will cut away damaged portions.
A dull/well used tap is my perfered method to chasing threads and cleaning gunk out of a threaded hole. They're accurate so not much risk of removing any more material than necessary.
I have some thread chasers and use them occasionally but sometimes they remove some or do more harm than good... I thought they were good quality but perhaps not as nice as I'd like.
Now cleaning male threads with a die... most male threads are "rolled" to form them, like on bolts, not cut. So to use a die to clean or straighten them will most always cut a little from the valleys. Not a big problem but you may loose a tiny bit of strength advantage that rolled threads have over cut threads, I usually wouldn't worry about it. Adjustable dies can be opened or closed a little to just fit and clean existing threads without doing any damage.
Grigg