I gave the Magni 3 a glowing review, and said that everyone getting into audio should own one. I stand by that. Moving up from the Magni there's 2 direct options. The Magnius, and the Asgard 3. These both have substantial power overhead compared the the poor little magni with it's wall wart of a power brick. The big feature difference between these in terms of physical features is that the Magnius is pretty much 2 magni in one box, and balanced, where the Asgard does away with balanced in favour of raw power through single ended output.
Balanced audio is quite common in microphones because it's power level is very low, and wire runs are long. This allows for EMI to be picked up in the wires, and balanced audio is able to completely cancel that out in hardware. Headphone amps probably aren't running 30 meter cables to your headphones. There are other reasons to run balanced such as if it offers both, it is built with balanced in mind. This means that something like the Magnius will have much less power out of it's single ended output than the balanced XLR. The Asgard is only single ended, and puts out full power from single ended. If you have only single ended headphones, then the Asgard makes more sense.
Balanced does have other advantages, however small. Once you start spending multiple thousands on headphones, start picking out every micro detail at insanely loud volume through a high end Delta Sigma DAC's, ect, it can make a difference. The Asgard 3 is about one thing. Make things sound like music, and give you and enjoyable presentation. It's integrated power supply offers a much better source than the Magnius' PSU, which is still a wall wart. Schiit has done an amazing job with their wall warts, but to get the price that far down on balanced architecture, corners had to be cut. The Asgard 3 has access to up to 500mW of class A bias on it's power supply before finally smoothly transitioning to class A/B, which is what the Magni/Magnius are always stuck on. If you haven't heard half a watt strapped to your head, that's amazing, because you'd be at least partially deaf. Most in the audio industry agree that class A sounds smoother and more pleasing than class A/B, and the Asgard 3 will stay in that range during any sane levels of listening. If you need balanced and all of this, move up to the Jotunheim, but the price goes up as well for access to balanced.
I'm not going to bother breaking this into low/mid/high. Across the board, the sound comes out smoother sounding. Not less resolving, not less detailed. Just more correct in ways that I had to hear to understand. Other than this, the presence of the bass, especially sub bass, comes through with much more impact, clarity and force. Punch and slam becomes headphone dependent at this point. On tracks like Bracelet - Fat Jon, the sub bass track is much more lively, and audible. Even Heaven - Aimer is weighty and has so much presence in the bass that I had to turn the volume down from what I was used to on the Magni. The high end was still as clear as day, even with a 3dB boost to the bass shelf at 50Hz on the Sundara, unlike on the Magni which started to show it's limits when I wanted to push that sub bass out, and it started to obviously struggle to push out any volume down there.
Moving directly from the Magni to the Asgard, the biggest things I noticed at first weren't even the sound. The Asgard on the desk is much more substantial in size and weight. The Alps pot for volume control is leagues better than that found on the Magni or Magnius as well. Their volume pots were small, not insanely smooth when turned, and a bit scratchy. This doesn't impact the sound they make once you aren't looking at or touching them, but it is something I noticed in use, and it does feel more premium. Not features I'd tell someone that you must buy this device for, but absolutely something I notice in real use, and had to note that I do actively appreciate these things. If none of that matters to you, just ignore this section.
If you love your sub bass, and have anything that is current demanding like a set of Hifiman Planar headphones or similar, this is a no brainer if you can make the budget allow it. If headphones in the $300 and under such as the HD6XX and Sundara are where you plan to stop, and you don't mind a bit of sub bass loss, it's hard to justify the extra cost coming from the Magni, but I'd recommend at least considering it if you want the extra headroom to hear other headphones above that price point. If you are ever near one of Schiit's physical stores, you can hear them both for yourself and decide. I personally wouldn't go back as the extra last bit of audible difference, as well as tactile feel of the device is just that much nicer.