The status is: Black first kills, White first lives.
If White first, the key move is the tesuji of .
See BQM 374 for a discussion on whether at a would be a better move.
The previous diagram also explains why should not be played as shown in this diagram. Because after , the situation transposes to the previous diagram.
Bill: Is better than simply capturing ? A difference game helps us tell. Let us set up mirror positions, and then show the resulting gote positions after Black pushes before capturing, but White, in the mirror position, simply captures.
Bill: But if White plays first, Black keeps jigo with .
The difference game favors Black, so Black should push before capturing, unless the ko situation dictates otherwise. Main line 2 is normally superior for Black to main line 1.