I have a Gungnir delta-sigma and Bifrost I multi-bit. The short answer, to my ears, is the Gungnir has "more". The bass goes deeper and has more detail, though it may not be as high in volume. That may be due to Gungnir bass being shelved down in level a bit comparted to Bifrost, or it could be Bifrost has a mid-bass hump. Midrange is more present with Gungnir, and vocals have slightly but noticeably more presence and intelligibility. Gungnir highs are sweeter and smoother. In comparison Bifrost is a bit rough around the edges at the top of the range. I use both of these DACs in headphone systems and since I don't pay much attention to sound stage when I listen to head phones I won't comment about that.
A summary could be the Gungnir is more extended, smoother/ more refined sounding and has more detail retrieval than Bifrost. That said, I don't feel I miss anything when I listen to my Bifrost. To be honest I bought my Gungnir simply because I was curious. Bifrost is fun when listening to, especially, classic rock, which is supposed to have a bit of an edge to it. It also adds some bite to brass instruments. Whenever I switch systems, I'm back in my comfortable groove zone, ignoring the differences between the two DACs within one song.
My Gungnir is currently on its way to California to have some bits added. I will be able to comment about the difference between Gungnir and Bifrost multi-bit in time.