I very much doubt that a few puny missiles will damage an Eva very
much (unless they were nuclear). 

veritechs use Reflex weaponry..which is WAY stronger than nuclear missiles

a Valkyrie can do evasive maneuvers

until the Eva runs out of power. No AT field. No Eva soon after.

eva's are groundbound....the valkrrie is a sure win

Eva's can use rifles. :)

valkyrie's use rifles all the time :)

Also, later on in the anime, there are occasions where Eva-01 operates
at above normal performance when it has NO power (at least no
conventional power).

valkyries can fun for 12 years without needing refueling :)



(Now, if the Eva has wings and an internal power source, it WOULD win

in almost every engagement.)

yeah..but it dosent....so it'll loose horribly :)