With the L2, the tube is CCS loaded whereas the BA the input tube is resistor loaded.
The L2 the tube is DC biased by a transistor shunt regulator, the BA output tube is biased by high frequency. There are merits to both DC and AC bias which does influence the sound greatly, all ill say is that Doug and Craig have implemented them creatively and effectively in their amps in comparison to the other headphone amps out there.
The L2 is capacitor coupled to the output transformer, the BA is directly coupled to the output transformer. Again both have merits and both have pros and cons, both approaches influence sound.
The above is just a sampling of the design philosophical differences between the two and are a big part of why the two sound different. I will say that both offer something in the headamp market that is fresh, creative, and different from anything else you would find.