A tumbler does make your brass look nicer. It also makes it go thru the reloading process easier and is not as hard to work. I also find that clean brass is easier to find on the ground after firing. You can get a Midway tumbler for around $50.00 and I consider it a worthwhile, but not absolutely necessary item to have.
I haven't been reloading for very long and didn't have a tumbler at first. I finally relented and bought the small Dillon model and really like what it does for the brass. Like maxwayne said, it's easier to see your brass at the range, I believe it's easier on the dies and it's easier to see defects in the brass like small cracks.
I think there's a sense of pride of pride of workmanship that enters into nice shiny reloads. It tends to say "quality". I know this is a personal bias, but when I see people shooting tarnished, smoke-stained brass, I kinda wonder about the quality of their ammo.
As was also mentioned, clean brass is easier on your dies and shows up damage a lot better.
If you load for a semi-auto rifle, a tumbler will be a "must-have" item, I can assure you that if you have 4-500 empty resized cases looking at you that need the lube taken off,you'll quickly find out that a roll of paper towels and some elbow grease is'nt gonna get it,(maybe, if you have a week or so...)they do save some wear on your dies, make finding bad brass much easier,and get resizing lube off rifle cases quickly,they are a very worthwhile item to have.
My understanding is that the petsmart stuff is just ground up walnut shells, the lyman stuff(red) is ground up walnut shells with jewelers rouge in it, The rouge DOES polish up cases nicely, Some people claim the rouge will get into your barrel and over time ruin it, I don't think that's true I've been using it for a long time,(bought a pile of it on sale) and have seen NO loss of accuracy in any of my rifles or handguns
I haven't seen it yet,The rouge itself doesn't stick to the cases,as a abrasive it is very, very,very, fine, rouge is used by jeweler's to polish soft materials like gold, silver, so not alot of material can be removed,if it did, they would'nt use it, and most steel dies are made from very,very,hard steel, if there is a wear factor here, it is a very small one, So,no, I don,t think it will wear your dies,