Hi, Jackie. 'happier' - piu' felice - is a comparison, it means more happy- happier than before, happier than yesterday, happier than you ...
More THAN happy is different, it's a casual phrase meaning very, very happy. No comparison with anything else - just really, really happy. (A: How is the ice cream? Happy? B: MORE than happy!)
Darn. Now I want ice cream.
Have a more-than-happy day. :)