It’s hard to say.
The only headphones I own that I would feel the need to drive from Hugo TT 2’s rear-panel XLRs are the Abyss AB-1266 Phi CC - at least to get the best out of them at loud levels. But at normal levels (say 105 dB peaks) even that isn’t really needed and they sound great straight out of the front panel.
There is a very slight stage benefit to using the rear-panel connections, and potential a hint of increased resolution, from the Hugo TT 2, but the difference likely has more to do with not having shared grounds for the headphone feed than anything else (typical for balanced headphone drive).
In terms of Hugo TT 2 vs. a Phonitor X/Yggdrasil A2 pair …
Well, from one perspective, a Hugo TT 2 is 1/3 the size of the Phonitor X. And a bit shy of 1/5th the size of an Yggdrasil. In fact you could run a stack of Hugo TT2, M-Scaler & TToby amplifier and still come in under the total size of the Phonitor X, never mind the Yggdrasil or the combination.
The Phonitor X is much more flexible … with multiple analog inputs and outputs, much more control on the crossfeed/matrix functions, has front panel access for both single-ended and balanced headphones and proper VU meters. So it can be used with more than one source (e.g. a DAC and a turntable). And it has more single-ended power than the Hugo TT 2.
The Hugo TT 2 is digital-input only. Front panel is single-ended only, and lower power. But the XLR outputs are more powerful than that of the Phonitor X, even though they’re lurking on the back panel.
As a DAC the Hugo TT 2 and Yggdrasil A2 are quite different. The Chord unit is slightly more resolving, has a blacker background, and a more “reference” presentation. The Schiit DAC is moister (it’s not really “wet”) or warmer in its presentation, hits a bit harder in the bass and has more convincing stage (unless you pair the Hugo TT 2 with an M-Scaler).
On pure sonics, if it was just Vérité I was driving, and I only needed digital sources, I’d go with the Hugo TT 2. I think Yggdrasil A2 -> Phonitor X -> Vérité would require using the Vérité pads for me.
If other headphones were involved that might change, and it is, of course, depending on what sort of signature you want (warm/neutral/brighter).
Both setups are very capable, and the value and flexibility of the Schiit/SPL combination is hard to overlook, provided you have the space and don’t mind leaving the DAC on 24/7.