I don't have a bagger unit so can't really give a good comparison between the two. But I'll give it a shot anyway.
I use the CR for leaves, but for clippings I just side discharge, cut frequently, use Gator blades, and the clippings disappear into the lawn. With a zero turn tractor (I know, this is the JD forum... sorry), dragging the big CR behind me kinda takes the fun out of the ZTT manueverability. Plus it means I have to have a place to store it fully assembled during the entire mowing season, instead of just during leaf pickup season, and I don't have a lot of garage space.
As far as leaves go, having a cubic yard of hopper is a definite advantage over 7 bushels of bagger. I get a LOT of leaves and even 1 cu yard at a time I'm still emptying the CR hopper of leaves 4 or 5 times during a typical fall cleanup of my 1/2 acre yard.
Doing the same with a 7 bushel bagger... there are about 20 bushels to a cu yard, so that's 3 times fewer dumpings with the CR if both condensed the leaves the same. But in my experience, the CR (with it's shredder impeller, combined with Gator blades on the mower deck) pulverizes the leaves up into dime size bits which are very compressible in the hopper. I would estimate you get 3 to 4x compression vs just bagging.
So that's maybe 10x fewer dumpings with the smallest CR vs a 7-bushel bagger. My yard during the fall would then require 40-50 dumpings if using a standard bagger, vs 4-5 CR dumps. But again, that's just a guess as I don't have a bagger to do a true comparison.
You should be able to find a used CR between $500 and $1000 if you can hold out for a good deal to come along. New, the smallest model starts out around $2000 after shipping, with no accessories. They are pretty tough units and stand up pretty well to being hand-me-downs. Mine's a real beater but still going strong. I'm the 3rd owner.