I am no fan of harsh treble believe me, but I have owned most of the headphones being discussed here. I never found the DT770 or 880 to be a problem in the treble, and I listened quite loud. That isn't to say that I haven't heard better treble presentation elsewhere, but I just don't feel they were in any way bad. My memory of the DT880, and I had the pleasure of the 600ohm model driven by an SPL Auditor, was of a very, very good headphone, a classic signature from Beyer as the HD650/600 is to Sennheiser.
I was lucky enough to have owned, for a time both the HD600 and HD800S, and have a wonderful La Figaro 339 with some gorgeous tubes. I was very lucky with the 339 and tubes. I also owned the HD650 at the same time as the DT880 and ultimately elected to keep the 880s over the 650, but it was a very hard decision for me to make. I really liked all of the HD series, I even have an HD700 on hand (a friends) right now, and that headphone is pretty nice once you do a little equalization it seems to balance out better and really is overall good and with quite a bit of the music I listen to, at times I found the HD700 to be extremely engaging and having me think, at this time this headphone is sounding amazing.
The sad thing for me is that when I had the HD600 and the great OTL tube amp rig, I was very lucky to have an opportunity to get a mint HD800S from a US based head-fi member, and the price was quite good so wonderful luck there. Once I had the 800S on, as much as I wanted to give the 600 more head time, which I actually don't have much of at home believe it or not, with the 800S I was hooked. I plumped up the bass, just a bit, not much, just enough to be effective and that headphone was cracking good.
But to end on the HD600 as I should, I do think that I would likely prefer it over the 650, not by a wide margin, but enough to know. Looking back to the entire HD catalogue, Sennheiser has just produced incredible headphones, a diverse array of signatures, and spread out in price-point so that much of the range was affordable. I haven't heard any of the 500 series HD models myself, but I feel pretty confident predicting I would also find many things to like in that series.