Rules question: high/low games with no qualification

[SumZero]

I posted a poll in the home poker forum on this topic and started to get responses, but I was curious what the various dealers and floor persons in this forum would think. The issue comes up much more in some of the wilder home game variations but can occur in 7 card stud high/low no qualify as well. The basic issue can be illustrated by considering the following two players who are heads-up all-in and at show down with:

Player A:

[A[img]/images/graemlins/club.gif[/img] A[img]/images/graemlins/heart.gif[/img]] 2[img]/images/graemlins/heart.gif[/img] 3[img]/images/graemlins/diamond.gif[/img] 4[img]/images/graemlins/heart.gif[/img] A[img]/images/graemlins/diamond.gif[/img] [A[img]/images/graemlins/spade.gif[/img]]

AAAA4 for high and AA234 for low.

Player B:

[K[img]/images/graemlins/club.gif[/img] K[img]/images/graemlins/heart.gif[/img]] 2[img]/images/graemlins/spade.gif[/img] 3[img]/images/graemlins/club.gif[/img] 4[img]/images/graemlins/club.gif[/img] K[img]/images/graemlins/diamond.gif[/img] [K[img]/images/graemlins/spade.gif[/img]]

KKKK4 for high and KK234 for low.

Who should win the low part of the hand?