I have listened to the DT 880 Pro (250 Ohms) and the X1 today, and a bunch of others: DT 990 Pro, K 701, HD 558, 600 and 650. However, the Beyers and the K 701 were in one store, the Senns and also the K 701 in the other store. So the AKG was the reference point.
I have never had a chance to hear the ATH AD 900 (X) - would be an interesting comparison.
I liked the DT 880 and the X1 the most. I'd say the X1 is a refined version of the DT 990 with a bit better soundstage and even more bass, while the DT 880 is the refined version of the DT 990 with more detail and an incredible flat response.
The K 701 was a big disappointment for my ears. Many people like its flat response and wide soundstage, but a few notice plasticy resonances in the mids. Me too. Pretty much. Dealbreaker-like much. Also, the bass is too dry on these for my taste. And it's far more quiet than its 60 Ohms suggest.
The Sennheiser HD 598 has more bass than the K 701, but it has a similar dry sound to it. More mid-bass though. The mids have a slight resonance and lean forward in the upper region. It's not as plasticy sounding as the K 701, but still not too pleasant. The soundstage is better than on the AKG, maybe best of the bunch. The upper treble is a bit less sparkly. It's a very good headphone for its price range (around 170 €) but for a little more, you can get better cans (e.g. the X1 for 195 €, or even the DT 990 for 150 €). The K 701 is a better headphone in the same price range if you can get along with the mids.
The HD 600 and 650 are a different price range at 300+ €. During my listening session they were better than the AKG but not better than the Beyers and the X1. Less soundstage than all but lots of detail, even though they are warmer sounding. Slightly slow bass but very balanced.
All in all, I think I'll get the Beyer DT 880. It had by far the most natural frequency response, clear and flat mids, natural soundstage, perfect fit and finish etc. It's better than I think a K 701 or DT 990 Pro or HD 580 (the "cheap HD 600", used for less than 100 €) + headphone amp could get. The bass on the X1 was too much for my taste and in comparison to the DT 880, something in the X1's mids is missing. I personally don't bother the "Beyer peak" in the treble - I barely notice it. Some might disagree. I think the X1 has a perfect treble.
My ranking of today:
1) Beyerdynamic DT 880
2) Philips Fidelio X1
3) Sennheiser HD 600 (close)
4) Beyerdynamic DT 990 Pro
5) Sennheiser HD 650 (close)
6) Sennheiser HD 598
7) AKG K 701 (close)
/edit: I think I won't get the Beyer DT 880 in 32 Ohms, but in 250 Ohms. I have read that it's loud enough for occasionally listening with a portable device at home. Mostly it will be driven on more powerful outputs. I don't have a headphone amp just yet - will see if I need one. The 250 Ohms version has the potential to improve with one and they sound more tight and clear in general.