I do enjoy owning both, a lot. I got the Hd600 first, but, before purchasing the HD6XX, I also read a lot of reviews which compared the HD600 with the HD650, with some preferring one to the other. The sound signatures of the two are indeed not very far apart, but the HD650s are slightly warmer, heftier and more "lush" in the mids and in the lower frequencies (which is not to suggest that the HD600s are necessarily "thin" sounding, or anything like that). Still both are excellent and very capable all-rounders for the types of music I listen to, and it helps that I use the HD600 exclusively in the office (along with my Hifiman He-500, which is another very capable all-rounder). Both of them respond very well to the quality of satellite components (amps/Dacs), and that of the sources that feed them, and when that quality is assured, they can hold their own quite well against cans costing a lot more than they do, and that is why they're both "classics" (some may say "reference" standard cans), in my view.
I also own the HD 700s and HD 800s, as well as the Audeze LCD-X, and Hifiman He-1000, and Edition X V2, and yet neither the HD 600 or HD 650 ever gives me the impression that I am listening to a particularly subpar set of cans when they're in use. Of course there are subtle differences between the HD 600/650s and the more expensive TOTL ones, but the degree of those differences never match the markup in prices, in my view. I am sure you have heard about "diminishing returns," but that is another story...
To return to you question, I certainly do not find the HD6XX to be "redundant" alongside the HD600, because it brings to the table a slight difference in flavor that I do appreciate a lot, depending on the type of music I am listening to, and I enjoy having access to both cans for the variety they provide, and the convenience of being able to use one of them exclusively away from home, at the office.