Diagrams repeated for convenience.
Willerz: Black a gives B two eyes, but after White b, Black's kill depends on what's to the right. So black can live. I think that White a kills Black, and thus lets white live, but I would need to check that properly.
Shaydwyrm: After this exchange, black is ahead 10 liberties to 5 (actually, black need not play 2 at all if there is no threat to connect on the right).
Shaydwyrm: here, though, threatens to create an eye inside black's group, so black must respond at (if at a then white 2, and black is behind 2 liberties to 5).
Shaydwyrm: Play might continue like this...
Shaydwyrm: ...and now it is evident that white is one move ahead in the capturing race. Part II follows the same logic, except that because white has one less liberty on the right, black is a move ahead instead of white. All of this is complicated a little if white can escape to the right, but if we make the fairly standard (though artificial) assumption that the rest of the board is empty, white can't gain any liberties that way.
Willerz: Again, Black a gives B two eyes, so black can live. This time the subsequent Black kill is unconditional. I can't see any way for W to kill -- if is at a it's a straight liberty count and White loses.