Well, I bought a Yggy so I can partially answer this question myself. However, I still do not have experience with a fully upgraded W4S DAC-2 DSDse model.
For starters, the W4S DAC-2 is a VERY capable unit. It has excellent build, features, an array of inputs and outputs, and can serve as a nice preamp with digital volume control. Really I have no complaints about the unit, the "is there something better" bug simply got the best of me after a while. So this is really a lesson of when to say "when" for me.
The reviews around the Schiit Yggdrasil are pretty positive. In fact, the hype is why I became interested in it. My uncle also has many high-end vintage pieces of Theta gear that I have heard in his listening room, so the Yggy partially being a modern rendition and upgrade to Moffat's Theta goals was very intriguing to me.
To get to the point though, I will have to say that either the hype around the Yggy is mainly that, or the base W4S DAC-2 is just that good.
When I did my comparison, I used my Sqeezebox Touch playing FLAC files going into both DACs via coax and optical (because the W4S does not communicate via USB with the SBT). I used an SPL meter and the digital volume control of the DAC-2 to be able to get a good volume match with the Yggy. My amp is an Eddie Current Balancing Act, so not only was I able to test the DACs individually, I could also have both connected to the BA via RCA and quickly switch between inputs for simultaneous comparison (albeit the SBT was connected to the DAC-2 via Coax and to the Yggy via Optical for this).
Let me start out by saying that I have had the pleasure of using other DAC and DAC/Amp combos, and I have heard differences between them. So, I am not in the camp that every DAC sounds exactly the same. I am in the camp that MOST DACs sound the same except for when the manufacturer/designer tweaks things to achieve a specific sonic signature or if the unit is just a POS. Meridian Audio, for example, has a very "British" hi-fi sound to their DACs. It is a signature sound... spacious, but very warm or rich, not ultra-resolving or crisp. If you have experience with Meridian, Linn, Quad, B&W gear you likely have an idea of what I mean.
Anyway, I fully expected to be blown away by the Yggy. After all of the positive feedback, I thought surely it would take my listening experience to a different level. Rather, what I heard was limited to a minor tonality difference that has an equally small impact on the perceived soundstage. Both the W4S DAC-2 and the Yggy are detail monsters, have very low noise floors, and get out of the way of the music. This is their goal by design and both achieve it well. I get no sense that any part of the recording is not being rendered. Besides overall form and features, where they differ TO MY EARS is a slight shift in tonality where the Yggy is a hint more "analog" sounding and the W4S DAC-2 is a bit more crisp and "digital" sounding (this is inherent in Sabre DACs). The difference is heard mostly in the treble regions. For instance, the cymbals on the Yggy sound a bit more real to me (I was a percussionist), whereas on the same track the W4S DAC-2 has a slightly harsher, more glassy presentation. Albeit, you really have to focus on specific track details to hear the differences. Similar differences can be heard in female vocals. I also thought the Yggy pulled out slightly more low-level or background detail, possibly due to the proprietary filtering. For example, on a live version of Lucy Rose's "Shiver" her male guitarist does some backing vocals. His voice is low and a bit raspy. I think the Yggy's more organic sound gave his voice some better separation from Lucy's, while on the DAC-2 his voice is more overpowered by Lucy's higher pitch.
In all, minor differences. Yggy is slightly more analog, organic or natural -- however you want to phrase it -- while the W4S DAC-2 comes off as a bit more analytical or digital in its presentation. As for all of the other things like air, space, 3D, soundstage, PRAT and the other things people normally like to toss into their descriptions, do not expect vast differences. Both DACs are incredibly good, and capable, and can cover the entire dynamic range of your hearing, and you'd be more than happy with either one I assure you.
The fact that you really need to analyze intricate details of a song to hear minor differences tells me that under normal listening -- you know, for pleasure -- you'd likely not be able to tell the differences between these two DACs. So which should you get? To me, they are both pinnacle pieces. I don't see any reason to spend more money on a DAC than for either of these. A fully decked out DAC-2 new is a little more than a new Yggy. If you need DSD and extra inputs, maybe that's the way you go. The truth of diminishing returns hits hard here. Buy for form and function and your personal pleasure, but again don't expect vastly different listening experiences. The differences are subtle enough. These things are designed by experts in their field. As long as the designers' goals are to produce transparent, accurate DACs, like they have here, it's pretty safe to say they are going to do the same jobs equally well. Again, my overall impression is that the differences are minor. The Yggy is slightly more analog, organic or natural and the W4S DAC-2 is a bit cooler, analytical or digital in its presentation. Both however sound excellent to me and both are the best DACs I have had in my personal system.
I personally think I am going to live with the Yggy for a while and let one of my DAC-2s go simply because I like the ever so slightly more organic sound of the Yggy.
This is my opinion. This is what I heard. I fully expect some people to say my opinion is BS. So be it. Apparently to other reviewers/owners, if the Yggy isn't good enough for you, you have to buy a stupidly expensive MSB DAC for $6,000+. Honestly, I have no idea what could be inside any DAC to make it worth cost that much.
I've had or heard DACs from the likes of Theta, Sonic Frontiers, Meridian, AMR, EAD, Threshold, Yulong, W4S, Schiit, Sony, ALO, Resonessence and more. Yes there are some that do things differently, but the journey to "better" is fleeting.
My full headphone system includes the follow for reference.
Sources: Sony DVP-S9000ES for CD/SACD - Squeezebox Touch for FLAC
DACs: W4S DAC-2 or Yggy
Amp: Eddie Current Balancing Act
Cans: HD800 (used in comparison) or LCD-X
Note: Yes, the Yggy had been constantly on for several days before listening. I have no reason to believe it was not at optimal temperature for critical listening.