I'm still the same old me, but surrounded by different landscape, a different set of people, different benefits, different challenges. My natal Cancer ascendant is, and always will be a part of my personality. Cancerian characteristics didn't disappear the minute I arrived in Oklahoma! Most of my relocated chart is compatible with natal orientation, important planets remain emphasised but in different ways. I didn't choose the new location; one might say that it was thrust upon me, by fate, and that fate was kind.
What I believe happens in relocation is that the fresh location adds an overlay, to highlight signs and/or planets and aspects which had previously been taking something of a backseat in the personality. Consequently the brighter light which, natally, had fallen on some signs/planets/aspects, becomes dimmer at the new location. Relocation simply causes re-orientation of the whole chart. I guess that transits to natal chart might be reflected more clearly, outwardly, in the relocated astrological house position, but retain some inner echo of natal house position. I have to admit to not having done much research on this particular point in my own chart, not being a keen follower of astrological house lore. Also, as the relocated Aquarius/Pisces cusp ascendant kind of matches my natal Sun which is semi-sextile-twinned by degree with Jupiter in Pisces - there's a similarity there to natal chart. I'm perhaps not the best subject for research into this particular corner of astrology.