The Asgard 2 can deliver more power.
The O2 has less distortion spec's but are not clear on the conditions. The Asgard 2 was measured under worst case conditions. but both are well below what a human can perceive.
The Asgard 2 has less noise even though the O2 lists a better number but at a lower output, although they don't spec the gain at that measurement, call that specmanship. Both are very quiet.
The Asgard 2 has better crosstalk figures,
Neither specify transient distortion (almost nobody does ), however, the Asgard 2 is a low or no feedback design which is less susceptible to this.They're probably both fine in this regard.
If your driving HE-500's the Asgard 2 is a better choice as to the power level being 1.0W at 32 Ohms and the O2 is 0.613W at 33 Ohms. The Asgard also delivers more power to high impedance cans.
The O2 is inexpensive and a good value.
I haven't listened to the O2 so I can't say firsthand, specwise it's nice as long as you don't need the power. I have an Asgard2 and it sounds very good.