Why is the Omega more desirable, your´s looks excellent?Cape Cod cloth is a metal polishing cloth. It will bring up shine and remove surface scratches, but won't give you a completely new appearance. You can find it on ebay. A Professional polish at a watchmaker could bring the case up like new, though I agree with the suggestion above that if you do go that route you ask the watchmaker not to go 'all the way' so that some imperfections are left.
A chapter ring is a small metal insert that covers the gap between the dial and the crystal. You may or may not have one in that watch. (I suspect not.)
I polished this stainless steel 50s Roamer with a Cape Cod cloth. It looks clean and shiny but some dings, etc. are left. It also has a chapter ring, which you can see in the photo. Your watch is of course much more desirable than this one.