Reply #1 Top
Putting money into Espionage allows you to gain intellengence information about an enemy empire, such as the amount of funds they have, or their current racial bonuses. At the highest level, intel is maxed out but does not give information about troop positions. However, investing further gives a chance to steal technology.

Putting money into Destabilization reduces the morale of the affected planets. While it might not do much damage, a little adjustment in morale can mean the loss of a senate position resulting in a huge penalty.

Is it worth it? It's your call, but a small amount over a long term can do wonders.
Reply #2 Top
Just stick the minumum amount into espionage every turn. It does more good than not by helping to avoid a couple of bad events. Besides, seeing the other guys' spending and bank balance is very helpful at times, especially in the midst of a destab campaign. Not too mention getting those exact bonuses. If I see a fool with a 150% weapons or something and it is still early in the game, it is time to go starbase hunting.