Interesting question, but it implies a false dichotomy, as if you're saying if one is happy, one can't be free, likewise that if one is free, one can't be happy.
There's also a false equivalence implied, as if the two concepts are equal.
What does happiness really mean? Happy to see you? Happy birthday? Happy to be here? You've made me so very happy? It's at best a nebulous term, pretty much devoid of any serious meaning in my opinion. I don't think one can ever honestly say, Well I've achieved happiness so there's nothing left to do. If someone tells me, "I'm really happy now," I think to myself, Just wait a minute, the feeling is fleeting.
Freedom, on the other hand, goes much deeper, and although opinions may vary as to what constitutes freedom, countless wars have been fought and countless people have died in its name. It's hard to imagine anyone willing to go to war or die for happiness.