I believe Lady Macbeth is more determined to have King Duncan killed. From the very first moment that she learns of the prophecy, she is plotting to get Macbeth on the throne.
"Glamis thou art, and Cawdor, and shalt be / What thou art promised"
The line doesn't guarantee that she is plotting murder, but the hint is fairly obvious. She's not willing to wait for Duncan to die of natural causes, so from that moment Lady Macbeth is plotting to kill Duncan. She comes up with the entire plan without any input from Macbeth. Lady Macbeth even tells her husband this fact at the end of Act I, Scene 5.
Only look up clear;
To alter favour ever is to fear:
Leave all the rest to me.
Probably the best evidence that I have for her determination to have Duncan killed is Act I, Scene 7. After the banquet, Macbeth tells his wife that he can't go through with the murder any more. Lady Macbeth won't have any of it, and she berates Macbeth and calls into question his honor and manhood.
Wherein you dress'd yourself? hath it slept since?
And wakes it now, to look so green and pale
At what it did so freely? From this time
Such I account thy love. Art thou afeard
To be the same in thine own act and valour
As thou art in desire? Wouldst thou have that
Which thou esteem'st the ornament of life,
And live a coward in thine own esteem,
Letting 'I dare not' wait upon 'I would,'
Like the poor cat i' the adage?
Her "pep talk" works, and Macbeth resolves to kill Duncan.
I would like to play the devil's advocate for a moment to my own statement above. While I do think that Lady Macbeth is more determined to kill Duncan, I have always found it interesting that she doesn't ever actually screw up the courage to do any of the murderous acts. When Macbeth said that he wouldn't go through with the murder, Lady Macbeth could have walked into Duncan's room and killed him. But she didn't. She wants him dead, but she isn't resolved enough to do it herself. It reminds me of kids in school. One kid wants something done, but he is too scared to do it. So what does he do? He convinces somebody else to do it in order to avoid any possible repercussions. I see Lady Macbeth like that a lot of the time. She wants it, but isn't willing to actually take action.