This is the only decision on a dog bandana that is about safety rather than looks, and it takes about a minute to get right.
What a tie-on is
A triangle with two long ends, knotted round the neck. It adjusts to any dog, it looks the way people expect, and it is the cheapest to make.
It is also a knot. It can be pulled tighter by a dog scratching at it, and if it hooks on a crate bar, a fence or a branch it holds rather than releases.
What an over-collar sleeve is
A triangle with a stitched channel along the top edge. The collar threads through it and that is the whole fastening — there is nothing tied at all.
If the collar releases, the bandana goes with it. If the dog gets out of the collar, there is nothing left round its neck. For unsupervised dogs this is simply the right answer.
Where snaps sit
Between the two: adjustable like a tie, quick like a sleeve. The only thing that matters is whether the snap is a break-away plastic stud that pops under load or a riveted metal one that does not.
If a supplier cannot tell you which they fit, assume the one that does not release.
A simple rule
Supervised and going home tonight: tie-on is fine. Crated, boarded, in day care, alone in a garden, or working in cover: sleeve or break-away snap, every time.