I saw KBv2 first, in the theater, and liked it much more than KBv1 on home video. I saw v2 again on Video, and still felt it was superior.
The Lonely Grave of Paula Schultz is masterful a masterful scene, and ties in wonderfully with the Bride's warrior training in Japan.
v2 also has some character development around Budd (Michael Madsen), Bills brother; and the shows the Bride's "compassion" as she defeats Elle Driver (Daryl Hannah).
Volume 2 is less bloody and much more intellectual than v1.
Volume 2 is very bloody, violent and twisted, but more intellectual.