Rabbi Chaim Drukman often brings the following parable:
If you meet a friend in a place where you expect to meet him, like at work or at shul, then it's nice to meet him, and you're happy about it, but it's not something so special. Now, if you go, say, on a hiking trip in some wadi or such, and then suddenly meet your friend, you're even more happy to see him, because you have added happiness from the unexpected situation. Finally, if you and your friend have drifted apart for some years, and you don't think you'll ever be in touch anymore, and then you get tangled up in a difficult or dangerous situation, and suddenly out of nowhere your friend, who you thought wasn't your friend anymore, appears to save you - your happiness will increase tenfold or hundredfold over any previous situation.
During other holidays, while our happiness is great at the wondrous miracles Hashem did for us - it was expected, more or less. Or at least, it didn't come as such a big surprise.
But on Purim we were in a position of "Hester Panim", Hashem hid His face from us. We were in exile, there was no Shechinah there, and we were in danger of being wiped off the face of the planet. In general, we thought Hashem had abandoned us. And then, out of nowhere, Hashem revealed His face and everything changed - "ונהפוך הוא", and we realized that Hashem is still with us. That's why on Purim and all of Adar our happiness is greater than other holidays.