The experience level is common for all your islands and it's constant, you can only increase it. It is the measure of your general game progress. You gain experience from absolutelly all game activities and new levels always give you new opportunities: new buildings, quests, etc.

The happiness level is different for all islands and it may vary. It can increase and decrease. Happiness can go up or down. You boost it with decorations and social buildings, and you lose it if you remove them. New happiness levels allow you to construct residential buildings and increase your population.