I just spent some extensive time listening yesterday to a few DACs (Chord Mojo included), a couple of sources, and a few amplifiers.
To save you some time, if you have no interest, I did not listen to the Bimby. I have in the past owned a Bimby, which was upgraded from a Bifrost Uber. And yesterday, I was listening to my current Bifrost 4490, which I personally upgraded both the USB to version 2 and the chip from the original 4399. In no short order, I have heard every generation of Bifrost. And I came to the personal conclusion yesterday that I will own the Bifrost no more.
There is nothing wrong with the Bifrost! I very much enjoyed my initial listening sessions with Bifrost Uber feeding into the original Valhalla paired with HD650 headphones. But by the time I was able to upgrade to the Multibit version, I had already purchased and owned the Gungnir Multibit. I tell my closest friends the story of the great purge caused by the Gumby, including Arcam irDAC, Bifrost Multibit, and Meridian Director. Each of those DACs had certain traits that I admired, but not on the whole - I like the Gumby on the whole.
And in my, likely controversial opinion, I believe each the Bifrost, Gungnir, and Yggdrasil are voiced. And having listened to the voicing of the Gungnir, I found it preferable to Bifrost, regardless of the chip goodness that I believe the Multibit upgrade to be. And similarly during my listening session yesterday, I decided not to re-acquire the Multibit chip in my Bifrost. I started my listening session with the Bifrost 4490 and a DNA Sonett, plugged into HD800S headphones. It was enjoyable, but not the plan for the day. I planned instead to listen to the slightly more forward treble presence of HD800 and Audeze EL-8C headphones. And upon switching to the HD800, I immediately noticed significant dissatisfaction with the sound. I would flip, back and forth several times between the HD800 and EL-8C, so I will not bore you with that part of the changes. However, once I'd switched first to Explorer2 DAC and finally to Chord Mojo DAC, I never changed the DAC.
This final DAC switch, to the Chord Mojo, recalled the great purge. It was extremely satisfying, regardless of headphone, regardless of amplifier, regardless of source. I learned yesterday what a great source my Android tablet could be - not possible with any of the Schiit DACs due to their power consumption through the USB interface. Amplifiers I used were DNA Sonett, Cavalli Audio Liquid Carbon, and finally re-listening to my Asgard 2. Due to the stacking, I'd always listened to the Asgard 2 via the Bifrost, but from the Chord Mojo, it had an entirely new sound. The depth of the sound stage was not at the level of either the Sonett or Carbon, but it was still a satisfying, fun sound.
So no, I have not listened to Bimby/Lyr 2 in direct comparison to Chord Mojo. But in my opinion, the satisfaction I get from the Mojo is more on the level of Gungnir Multibit combined with other amplifiers, of which I would include DNA Sonett and Cavalli Audio Liquid Carbon. I personally would not use Mojo directly with my HD800 (just a personal preference regarding the more forward treble sound from the Mojo), but through an amplifier I found it to be quite satisfying. And into headphones for which it works, Audeze EL-8C is such an example in my case, it is quite satisfying all on its own.