I own both and I like each for different reasons. The RME-ADI 2 has a large amount of built in functions to adjust the output and has a nice software interface they call "ADI-2 Remote" that makes it easy to change settings, parametric EQ and other customizations. See here:
https://forum.rme-audio.de/viewtopic.php?id=37784
RME is a pro-audio company and some of the the audio-mixing functionality carries over in the ADI-2.
I like the Bifrost 2/64 in that it seems to have more resolution and a pure processing of the music in it's non-oversampling (NOS) mode. The Bifrost 2/64 only has two modes, NOS and Schiit's proprietary signal filter.
The main difference between the two is the digital-to-analog conversion process. The Bifrost 2/64 is a resistance ladder R-2R configuration on a chip which they call their "True Multibit" architecture. The RME uses delta-sigma processing with either AKM or ESS chips similar to many other DACs.
From Schiit: " we named it True Multibit™ because there’s a lot of confusion over what is really multibit and what isn't. Some companies refer to multilevel delta-sigma D/A converters as “Multibit” DACs. While kinda-sorta-maybe technically correct, this is pretty misleading. 2 to 5 bits of actual resolution plus massive amounts of noise shaping is not true multibit. Hence, True Multibit. We use True Multibit to denote DACs that have 16-20 actual bits, rather than multilevel noise-shaping delta-sigma DACs, coupled with our unique combination of time- and frequency-domain optimized digital filter, based on math first proposed by Western Electric in 1917, and developed into usable algorithms by a team that included a professor emeritus of math and a Rand Corp mathematician. It’s unlike any other digital filter today, and we believe it provides the closest thing to a true interpolation, while retaining the original samples as closely as possible.
Some reviews of the Bifrost 2:
https://www.head-fi.org/showcase/schiit-audio-bifrost-2.24927/reviews