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. To gain happiness points, you should always build new decorations, social and entertainment buildings for your villagers. New happiness levels allow you to construct residential buildings and increase your population. Note that the number of your workers cannot be higher than your happiness level.