aaaah i see what you did there. took me a while but i got it in the end.
regarding my final point i was merely referencing that even tho dante has been rebooted. at his core he is still the same dante (personality wise). both he and DMC3 dante are rash, aggressive, witty and over all awesome.
Going based on what Tameem said, and how DmC Dante was in E3 trailer 2010 - i'd say their core is not the same.
DmC Dante E3 2010:
Angry and aggressive. And Tameem said he is also dwiggling between good and bad.
DMC Dante:
Not aggressive and likes to kill demons in a playful manner.
Perhaps you haven't noticed but after E3 trailer there was no signs of DmC Dante continuing his smoking habit that he was given. And the angry side of him disappeared. And he became more like DMC 3 Dante. He also received white hair plus red jacket through Devil trigger.
Comparing E3 Dante and DMC Dante - their core comes off as different. Furthermore it took a year to come to the E3 character design for DmC Dante, so one should ask "Why is DmC Dante all of sudden less angry and more like DMC 3 Dante?".
Answer: For same reason Tomb raider and DmC are reboots and not new games, DMC and DmC Dante have been made similar to not alienate fans.
while lady and kat dont seem to share any personality traits. take the trailers for example. she tells dante how to leave, not to kill all demons like DMC3 lady would have. she hated demons and wasted no time in trying to killl dante and vergil when she found out what they were. kat on the other hand shows no hint of malice towards dante. im aware that this part of my theory is subjective but it still stands.