The evil alignment has very strong economic and military advantages throughout the game.
Early game, before Xeno Ethics is researched, evil colonization choices usually provide the best benefits.
Mid game, the Mind Control Center provides a huge +100% empirewide economy boost, and the Artificial Slave Center offers a special +50% empirewide military production bonus that is fully multiplicative with other military production bonuses. These buildings are expensive, at 1000 and 800 production units respectively, and require discovery of Concepts of Malice, but their power is unparalleled. Furthermore, the psyonic weapons are very space efficient for their location in the tech tree, and their cost is comparable to the same firepower of similar-era weapons. Plan on gaining one of these weapons soon after the end of the colony rush to overpower a neighbor.
Late game, the free Starbase upgrades allow you to send fleets of constructors to easily fortify a position with strong military starbases. Whereas non-evil races must spend thousands of BC to create a stronghold, you can make insanely strong bases at the mere cost of the constructors. Place them to overlap a fortified planet you wish to attack so when you invade, your ships gain the military bonuses. Also, building up a heavily fortified starbase (of any type) within enemy territory will often draw fire from enemy attack ships. Depending on the difference in firepower between you and your foe, the starbase may easily take out entire fleets before being destroyed, leaving less for your attack fleet to worry about.
Alternatively, if you wish for an influence victory, the free upgrades help mitigate the cost of upgrading starbases. Or, if going for an alliance victory, team up with other evil, militaristic races such as the Yor Collective or the Drengin Empire to knock the do-gooders out of the universe. In either case, the stronger weapons can be useful to raise your military rating to keep you from being attacked.