I'm on the verge of selling my Schiit Lyr 2 so that I can buy a Jotunheim but I thought that I might first ask this august body whether anyone had experience with both and could compare the two sonically. Feature-wise favors the Jotunheim because of the balanced output and because I don't have to worry about leaving it on. This is for my upstairs system which uses a Bimby so I don't need to consider the DAC module, just the amp.

I know more people than myself compared these two. This was my only focussed listening to the Lyr 2. Perhaps @Psalmanazar can add some notes, of what he heard via the HD650 headphone. I listened only with my HD800S headphone. And last, note the source was a Bifrost Multibit, fed input from a disc player. Thank you @kendavis for the disc player source, so we could quickly plug into something with which we are familiar. The Bifrost I have not hear or owned in quite some time, but I suspect it is only a small variation between it and my more familiar Gungnir Multibit source.
 
Impressions - Lyr 2 is warm, warm, warm. First warm is the box is almost untouchably hot. The hottest Schiit box I currently own is the Mimby, and I own a few of the ones that supposedly can warm up, like Ragnarok. No way, no how, does the Ragnarok ever get as warm as this box. I'm currently in debate mode of "Do I keep" HD800S, due to some recent headphones I have heard, which are changing my mind in regards to how good HD800S is. Particularly on the bass, which is not as deep as it should be. The second warm is the Lyr 2 warmed the bass one step further, which I liked. But then there's that last warm - it also warmed the treble, which I definitely did not like. Perhaps heard through an HD800, which could use a little warming of both the bass and treble, I might have enjoyed the Lyr 2 more. Through my HD800S, the Lyr 2 turned the world-class headphone (circa early 2016, late 2015) into something very warm, which I did not recognize.
 
Impressions - to my ears, the Jotunheim lets the headphone be exactly what it is. With the Bifrost as a source, I hear a very good headphone, down to the point in the bass where it loses to the newer generation of headphones. The bass is tight and punchy. There's just not enough quantity. And that is due to the headphone, and not the amplifier. I think I'd rather seek newer headphones, with better balance, and the Jodie.