I think Lady Macbeth is far stronger in nature than Ophelia because Lady Macbeth possesses the quality of pursuing a goal through convincing her husband to murder. Although there are unfamiliar, and supernatural circumstances, from Act I scene V onward up to Duncan's murder, it is lady Macbeth who has guided her husband to murder through her powerful eloquence:
I have given suck,and know
How tender 'tis to love the babe that milks me:
I would,while it was smiling in my face,
Have pluck'd my nipple from his boneless gums,
And dash'd the brains out,had i so sworn
As you have done to this.
although at last she surrenders to her essential femininity, she is powerful.
On the other hand, Ophelia is a passive character. She does not share Hamlet's misfortunes, she unwillingly listens to her father, she has helped the conspirators to entrap Hamlet to speak out the truth of his insanity. So,she seems to be rather a frail, helpless and powerless creature.
I may be going out on a limb, but I would say that Lady Macbeth and Ophelia are equal in "strength." If we define "strength" as the ability to withstand under pressure, then my opinion is derived by what auntlori so equally said in that "Death is their great equalizer." Had this been a Celebrity Death Match, then my money would be on Lady Macbeth -- she did assure she would bash her baby's brains in if she promised, afterall.
All kidding aside, Lady Macbeth may appear to be the stronger of the two, considering her position in society: married, Queen, elder; however, both Ophelia and Lady Macbeth suffer from the same vulnerability - their fathers. Lady Macbeth was originally the one who was supposed to kill King Duncan; however, "hath he not resembled [her] father as he slept, [she] would have done it," but he did resemble Daddy, thus she passed the daggers to Macbeth. Ophelia makes her final crumble into madness after the death of Polonius. Daddy depression strikes again.
We are also quick to judge Ophelia for allowing herself to be bullied around by Laertes and Hamlet, but we forget to not read with our own eyes -- we must read with the setting in mind. Lady Macbeth seems immune, at first, to this "ancient rite" of a paternally-driven society; however, as soon as Macbeth becomes bloodthirsty and self-indulgent, he stops paying attention to Lady Macbeth, and she crumbles thereafter.
While I always visualized Ophelia as a ragdoll in a constant state of tug-of-war, she did the best that her society would allow her to do. Lady Macbeth stands up to Macbeth better than Ophelia does Hamlet, but in the end it is "out, out brief candle" for both of them. The fact of the matter is that we only count the end, not the means.
I'll agree with everyone so far and say that Lady Macbeth is probably the stronger character of the two, and I can think of a few good reasons for that.
First, Lady Macbeth is older and, having lived and experienced more, is better able to cope with life as it comes. Because of her father's position, Ophelia has grown up in or around the Danish court--a fairly cut-throat place for adults but a rather sheltered place for the young.
Second, Lady Macbeth is married. There is a certain securtiy to being in that kind of committed relationship. Ophelia is a young girl experiencing the emotions and insecurities of first love.
Third, Lady Macbeth is independent. Ophelia still lives in her father's home and is therefore subject to his requests and demands. She has not had the opportunity yet to make her own decisions and live with the consequences of them.
Now, all that being said, they both commit suicide. That may be seen as both weakness and strength. Death is their great equalizer.
I have to agree with both of you on your arguments. Lady Macbeth is stronger in her initial pursuits, but proves weakness when she is unable to commit the act herself or deal with the consequences of their actions. She is strong in character initially, because Lady Macbeth is considered equal to her husband. "This have I thought good to deliver thee, my dearest partner of greatness..." (Act 1 Scene 5). She also is the one who ultimately convinces her husband to murder.
In analyzing that initial character in both Lady Macbeth and Ophelia, regardless of missing the similar relationship, I do not think that Ophelia would be able to follow through with the power that Lady Macbeth initially has over her male counterpart. She shows weakness right from the beginning, with her inability to keep anything from her father. She also is very quick to succumb to his requests in keeping away from Hamlet.
If we were to compare the relationship between Ophelia and Hamlet to Lady Macbeth and Macbeth, to come up with an answer on who is stronger, I still believe Lady Macbeth would win. Lady Macbeth and Macbeth have a partnership, while Ophelia is very easily manipulated by Hamlet's act of madness. I strongly feel that Lady Macbeth is the stronger character, because of the relationship, as well as the character from the beginning of each of the plays.
While Lady Macbeth and Ophelia are quite different regarding their positions and power, each is dependent on the man in her life for her happiness, sanity, and well being. Lady Macbeth is strong as long as she and Macbeth are companions. Once that relationship grows distant, Lady Macbeth crumbles. She maintains a convincing facade for awhile, but she cannot sustain it. We never see Ophelia in a similar type of relationship; we see Ophelia when Polonius orders his daughter to break off her relationship with Hamlet and Hamlet's vicious retaliation to Ophelia's following these orders. Ophelia begins the play comparable to Lady Macbeth's state of mind in Act 3. Neither is happy, and insanity is just around the corner.