I ran a test in the early game, and here are the results:
- For 150 happiness: the homeworld remains happy for 6 turns, is Indifferent the next turn, then becomes Happy against, and so on. (I checked for 120 turns)
- For 170 happiness (150 Environmental Resistance, the Artisans Culture, and 150 happiness): the homeworld stays Happy for 100 turns, and so it seems the value needed to fully offset natural decrease. (But you will not go to Jubilant)
These results are a bit better than what I expected, and it seems that +5% happiness does slightly more than increasing the happy people by +0,1% a turn. (+2% per turn is needed to offset natural decrease) But the effect isn't impressive, as other events would likely alter happiness. Thanks for mentioning this bonus about colonizing planets Primitive, I now understand why I am always at Jubilant, even with 50% happiness.
(bar such trivial events involving enemy fleets, troops and the Primitive one)
So raising happiness would give a small boost to your Empire by helping a bit to reach Jubilant status (other events or troops/UPCs are needed though), and would help to reduce the happiness loss when harmful events happen. However, once again, if these events are truly nasty, 150% happiness will not help much and you *will* be in trouble if you don't have many troops and UPCs able to keep your subjects peaceful as an armada is heading their way.