ANY rod can damage the bore if it's not used with care. You need to think about what you're trying to accomplish by cleaning, and what can happen along the way. You need to develop a technique that will get the rod through the bore with a minimum of flex, using a guide is the easiest way but I use my fingers tas a guide on a Handi.
One way to cause damage would be to induce enough flexing of the rod either inside the bore or at the chamber; even when using a softer material such as brass damage can occur by abrasion, as for example happens if there are tiny bits of abrasive material on the rod. The primer residue is very hard and abrasive. The line-type cleaning kits can wear the chamber or the muzzle too, if they're not pulled straight through and are allowed to rub the metal. friction-caused heat can damage metal too.
JMHO, but I think that it's best to use a rod sized correct for your bore, together with a good pierce-type jag and cotton patches, all properly sized for the bore you're after.
I use a 17-caliber rod and jag double-patched to clean my CZ rimfires, which have very tight bores. The 17-cal rod would work fine for 20-caliber bores too. I use the 22-cal. rod for all fo my other rifles, including my 45-70. I
I like the Dewey stuff but I haven't looked at the Tipton rods to see if they will accept the Dewey line of jags; I suspect that if they don't there are adaptors made by Dewey that will allow their use on the Tipton rods.
I like the Dewey stuff because of a lot of little things--for example the edges of their jags are radiused this allows them to be withdrawn back thriugh the bore after the foreward stroke passing smoothly ovet the crown. I like the pierce or spearpoint type jags because the dirty patch will not be pulled back through the bore. For polishing with flitz or simichrome a patch wrapped around a used brush works for me.
I think that if I were looking for a new outfit today, I'd go with the Tipton rod I think the bearings in the handle are a bit better than the Dewey. The carbon-fiber is probably better than coated steel, which is what the Dewey rods are made of.
I think that if you invest in a good quality rod you won't be sorry--I stalled for years due to the "high cost" of the better equipment. Then one day I was at a buddie's house and we were cleaning our rifles and he let me try his outfit. I sent away for a Dewey rod shortly thereafter.
A good rod and the properly-sized jags and patches will allow you to feel the inside of your rifle's bore much better. This can really let you get to know your rifle's bore.