It would be an interesting match-up, but with one slight problem.  While
the EVA-01 has a mind/soul as you put it, the Valkyrie/Veretech Fighter is
a mixture between man and machine.  The strange powersource, protoculture,
is what links man and machine.  Example: while moving the leg in
battaloid/humanoid mode is done by depressing the footpedal, the little
minute movements, ie balance, etc is performed by little telepathic sensors
in the pilots helmet.  In Macross plus, one of the test fighters ran by
total telepathic interface.  It's not that hard to assume a veretch could
gain a life on its own by being used by the same pilot over and over again.
Then we would have a truly interesting match-up.  The EVA's are orgainic,
the veretechs are inorganic with the capability of picking up orgainic
brain-wave patters and using them in movement.
        Anything could happen in that fight.