An old post on the "equipment" part of the board discussed how one individual made his own rings out of marine plywood. I took inspiration from this, as I'm a cheapskate in the truest sense.
I went to home depot and splurged on four 3/4" plywood rounds, some woodworking epoxy (dries harder than the wood itself), some sandpaper, and some weather sealant. I glued the plywood together so that I now had two 1.5" rounds. I used 2.5 and 5 lb plates as a template (couldn't find a compass), and used a jigsaw to cut out the rings. I used a hasp bit and my hand drill to work the wood into what my wife called: "Flintstone-looking" rings. Then I went to work with the sandpaper, and rounded, smoothed...
Now I use them all the time. I can hook them up to my pullup bar inside, or to my tree outside. Someday, I might buy real rings, but for now, I have less than $13 invested in some beautiful (to me) equipment.
There is no comparison. The chinup bar is great for a lot of things. Rings are indespensible for others in my humble opinion.