Okay, so a little comparison. I'll keep it brief as I don't have the M1060 anymore and it's not stock. Also, my M1060 did not exhibit ringing at 5kHz to my ears, YMMV here.
I thought the target response curve of the M1060 was pretty good, a warm take on neutral. The midrange and lower treble were slightly accentuated and could be a problem with the wrong associated gear. There were a couple issues with the M1060 that led me to selling them. The irregular frequency response (stock), comfort with the bumps in the suspension strap, and a "veil" to the sound. What I mean by veil is that the sound seemed too distant or behind a layer of cloth. This was NOT fixed by removing the protective earside driver cloth material, that just made them harsh. I think the pad distance and slotted design didn't jive with my personal preferences. Now that I think about it, that's probably the reason I don't care for Audeze headphones either, as they also have a slotted design for the housing. Personal issues/preferences aside, I can see these being a pretty substantial step up from most other headphones in their price range IF you get a good pair. And that's the problem, quality control. I might suggest people look at the HE-400i or 400s as an alternative.
The AR-H1 screams quality compared to the M1060, and it should being double the price at $599. I'm not sure about weight differences but the AR-H1 is more comfortable for me although the pad depth is barely to shallow and my ears graze the metal housing. The suspension headband is pretty good but you might still get a hot spot after a couple hours. You can push it up to relieve the pressure and I'm sure the elastic will loosen up with use and be less of an issue, same for clamp.
On to sound...
These two headphones both have good bass quantity and extension. Were they differ is the midrange and treble. The AR-H1 has a dip at 4kHz were the M1060 has a peak shortly after that. The dip at 4kHz isn't as pronounced since your ears are so close to the drivers and they are not angled. The leather pads also reduce the treble output so the peak at 10kHz is also not as bad as the measurements show. This frequency response creates a very wide and deep soundstage, one of the largest I've heard, up there with the HD800. There is excellent clarity and air with the AR-H1 which I found lacking in the M1060. Both have kind of a looser bass compared to ToTL headphones but extension and quantity are excellent staying pretty neutral.
I prefer the AR-H1 especially now since it's had more hours on it. It started out kind of harsh but I would keep coming back to it for an hour or so every day. It's now a great alternative to my modded HE-6 when I want something a little more lively for rock.
Comparison between AR-H1 and M1060 stock:
M1060 Waterfall: Note the excessively high and long "ortho wall".
M1060 Waterfall: Much cleaner than the M1060, the ortho wall seems tensioned a little looser at ~2kHz and is at a lower amplitude.
M1060 Impulse Response: Very ragged with bounce back up so there is some issues with diaphragm movement and decay.
AR-H1 Impulse Response: VERY clean, one of the best impulse responses I've seen on par with the HD800.