So the DT880 will give stronger sub-bass, and the HD650 will give stronger mid-bass?
Am I right in thinking that very few tracks actually have any sub-bass in them though? For example, if I listen to rock or metal music, even the kick drum, bass guitar and low palm muted guitar (the lowest sounds heard in rock or metal) fall under the 'mid-bass' category, don't they? None of them have frequencies that actually go down as low as the 'sub-bass' category? Only very low sine sweeps in the bassiest of electronic music actually have any sub-bass, isn't that right?
So, since the HD650 has stronger mid-bass but weaker sub-bass, it will sound much bassier than the DT880 on pretty much all genres, because no genres apart from highly specialized bass-centric electronic music actually have any sub-bass content anyway?
Lots of instruments, reverbs, echos, and end roll offs of a string or drum instrument have sub-bass in them. Load a digital equalizer and play some music and watch the bars. Even one of those will show some 40~60hz tones bumping pretty often. I notice it immediately when they're not there. But I'm a sub-bass head, I love everything under 50hz or so. I have acoustic music (DiFranco) that even has some sub-bass thumps just from different effects, tons of music has things like a big kick drum, or even a gentle thump on a cello instrument body, etc. Even classical; hell, especially classical.
Sub-bass is not just part of electronic and other assumed "bassy" music. There is mid-bass and sub-bass in nearly all music. If sub-bass is missing, jazz and classical to me sounds very lifeless and hallow, it's amazing how it's there and don't realize until it's gone.
But I will say the difference between the HD650 and the DT880's bass is not night and day or anything. We're talking subtly different. The main stark difference that is very noticeable on the other hand between those two headphones is that the Beyer is brighter (higher treble peaks) and the HD650 has a very apparent treble roll off so it sounds darker, more mellow, less sugar on top.
I keep thinking the HE400 would be absolutely wonderful for your needs as it does literally everything well.