My question is regarding the role of children towards their parents particularly in old age.
1) Firstly is there a difference in the duties towards parents for a son and a daughter? Meaning do sons and daughters have different duties towards their parents.

In South Asian culture a daughter once she marries is expected to only look after her husband's parents while no duty is expected towards her own parents.
Whereas for a son since he has to go out and earn and hence is not at home it therefore becomes his wife's duty to take care of his parents as he is financially providing for her . Is this the islamic way of life?

No there is no difference between sons and daughters when it comes to caring for their parents. It is an equally shared responsibility. The expectation that the daughter in law only serves her husband’s parents and has no duty towards her own parents is not an Islamic way of life. She has a great responsibility towards her parents. She still has a duty to serve them and help them if they need help.

Now if she lives in a culture where it will make a big problem for her if she serves her own parents, and this will create tension with her husband, then she should be wise and creative and avoid such tension. She can figure out indirect ways of helping her parents. Or serving them in a way that won’t cause tension with her in laws. But she definitely should try her best to serve her parents just like she takes care of her husband’s parents.