Per Unit System: what details am I missing
Your work is good.  You are using 2 different voltage bases to get your results (pasted in below).  That is why they are different in per unit.



If you take the results of your calculation using the phase-neutral voltages (Va-Vb) and convert them to the ph-ph voltage base you used, then they will agree.  In other words, the results of Va - Vb is 1.73 per unit in magnitude.  That is on a voltage base of 220kV/1.732.  To convert that per unit result to the ph-ph base you used above, multiply by (220kV/1.732 divided by 220kV).  

The ph-ph voltage base is root 3 larger than the phase-neutral.  When working problems - do not mix.  Just use one voltage base and carry on.  That way, when you convert back to actual volts you won't make a mistake.

UPDATED:  Showing base calculations.