I think men and women both yearn to receive unconditional love. I think at their core both yearn for relationships where unconditional love is the basis. I think both desire to know and feel they are always loved, in every moment, regardless.
Very few men and women seem to consciously know and live the kind of love, that is unconditional, that is regardless. Maybe some know it for a bit, as a parent to their child. I believe most men and women never consciously evolve beyond conditional love.
So, agreements are made, usually unspoken, of I'll love and accept you, if you love and accept me, or please me in this way. It can become a trap of trying to please others, to try and satisfy emptiness inside oneself. It will never work.
Ultimately, loving oneself, and entering a relationship from overflow, vs emptiness is the key.
Do men and women "love" differently? I think they barter conditional love differently. Both what they give, as well as what they want, in return for their "love," varies individually, by gender and even culture.
As far as unconditional love, for the men and women that are aware enough to consciously live and love from that place, I think it is a gender neutral capacity.
I believe unconditional love is what we all most deeply wish to experience and wish our lives to be filled with.