Neither - I think that strength is defined differently depending on the situation or circumstance. We say that some one, either gender, is physically strong when they can do things with their body that the average person may not be able to do. But, we also define strength as being able to withstand - emotionally, psycologically, etc. - some circumstances in life that many would find it difficult to face. We consider people that do not cave in to any/every other person's idea/beliefs to be socially strong - staying true to his/her own beliefs. The situation determines the characteristics required for strength- not the gender. (Of course, this is my opinion with the assumption that there is some level of intelligence of all parties involved. I think that responses to this question would vary greatly among the different socioeconomic groups of society.)
Physical strength is often defined differently, such as on police and fire fighter tests. It is recognized that woman can literally carry less. I know that some women are stronger than some men, but if it is about biological differences that seems to be accepted. There are women who seem to be able to move beyond their body's natural limitations. I think that woman often have to endure a lot, and there are many strong women who are strong in different ways. If a person, man or woman, really wants to do something than we are unstoppable.
I think the way we regard and think of strength depending on the gender of the person we are referring to owes a lot to the gender stereotypes that we have in society. It is interesting that when we associate strength with a woman, we normally do not mean the same physical strength as we do with a man. Instead, we normally refer to a strength of spirit or courage or determination rather than exterior strength.
Gender is probably the most powerful way of categorizing and thus stereotyping people so I do believe that nearly everything (including strength) is defined differently depending on gender.
In my view, traditional society views don't place much value or focus on a man's emotional state, challenges, or triumphs. He is just automatically expected to be "strong" in this area, not cry, and be emotionally balanced at all times. How many slang phrases are out there that imply that a man is automatically emotionally strong and fearless? ("Man up" comes to mind)
Thus, when society defines a man's strength it is, in my view, usually referring to his physical prowess, or even his ways of overcoming the odds and gaining financial and professional success.
In regards to women, society may refer to her as strong if she shows the stereotypical male characteristics of not crying, being fearless and not showing any other outward emotion besides aggression or anger.
Yes our Society defines strength differently for men and women. Strength in a man is usually physical, while if a woman is especially physically strong, she is seen as not feminine. Strength for a women is emotional, though this is seen as unmanly in men.
In terms of intellect if a woman has a strong brain, again she is looked at as not being feminine or not knowing her place. A man with a strong brain may also be looked at as weak, if he is not physically strong enough to meet societies manly standards.
I do not think strength is defined according to gender, but it is a stereotype. Men are presumed to have a great physical strength, and women are considered to be more emotionally strong. These might prove true in some cases, but it is not true in all cases. Nor should the genders be judged if they show strengths in non-stereotyped was.
Since there is no official definition of what constitutes strength for men and women, this is mainly a question of perception -- how do we think that society defines strength for men and women.
To me, strength in a woman is stereotypically seen as the ability to persevere. We hear about the long-suffering mother or the supermom. In both cases, the woman's strength is seen in her ability to deal with the stress of rearing a family and of dealing with the demands that society places on her.
For a man, strength is measured more through outward things. There is, of course, physical strength which is still valued in men even if they do not need it to do their work. But there is also economic strength. A man's strength is often measured through his ability to make money.
Again, these are simply my perceptions of society's expectations. There is no definitive right answer for this.