Yes, the HE6se is more technical for sure. It's more articulate/detailed and the bass hits harder and is more immediate compared to the HE560 v4. Imaging is also better on the 6. I'm definitely not arguing that the HE560 is a better headphone, just pointing out the similarities.
In fact, with the same pads, I don't hear any major differences in sound sig between the two. They sound to my ears (and measure) very, very similar, technicalities aside. Both the 1khz and 5khz regions are within a db or two of each other on my sets when using the same pads.
Disclaimer: Homemade rig, not comparable to other rigs, etc., etc.
Ignore the elevated bass on the 560's measurements, I accidentally left my bass shelf EQ on and I'm too lazy to do the measurements again.
Both with the Pelipad
Both with the 105mm velour pads from AliExpress (what I usually use on my HE6se)
So is the HE6se v2 a better headphone than the HE560 v4? Yes, absolutely. But the 560 is half the price, lighter, and much easier to drive, with less worry about driver QC while maintaining a similar overall sound (albeit, less technically capable). I think it's an option for someone who it turned off the HE6se for any of the aforementioned reasons.
EDIT: Just to be clear, while I think the HE6se v2 has a technical edge over the HE560 v4, I don't think it's huge. Maybe only 10-15%. It's certainly not double, as the price would suggest. Law of diminishing returns is alive and well here.