Together with Face of the Ancient it was one the best happiness-providing buildings available in the game until update 1.95, providing much more happiness per tile than premium decorations and even premium cultural buildings. Update 1.95 reduced the happiness value to only 56% of the original, thus making it only a bit better than regular decorations and worse than premium ones.
It can be used as a quick, free boost to happiness for quests requiring increased happiness.
The Gate of the Sun God can be upgraded by Gate of the Sun God Upgrade Kit item. To upgrade the Gate of the Sun God, use the Gate of the Sun God Upgrade item on the Gate of the Sun God that is already situated in your city. Its upgraded version will then be placed directly on the same spot in your city and the production timer will not be reset. Note that the upgraded building will be from your current era, even if the old one was from one of the earlier ages.