I really enjoy the trifecta of weapon types with their specific defenses. You can choose to use kinetic, laser or missile weapons and each has a specific defense technology. You can match up your defense and weapon research to whatever your opponent uses, but that leaves you possibly open to another empire who uses different technologies.
Does the game reward specialization, or is it possible to do well with jack-of-all-trades ships?
Specialization is rewarded, but not excessively so. If you specialize in laser weapons I can just as well specialize in energy defenses while boosting kinetic weapons as my own specialty which ignore energy defenses and are only deflected by kinetic defenses.
You can do a jack of all trades, but as in anything a jack of all trades will be master of none. A loadout of mixed weapon types and mixed defenses is inferior to a correctly configured specialized attack/defense setup but superior to a badly configured one. If you have balanced defenses (kinetic, energy, missile) and your opponent only has lasers, the tonnage devoted to the other defense types are useless.
But!
You have to also take into account the fact that different weapon types are boosted by different effect cards and different phases of combat. Missiles are very powerful in the long range portion, kinetic weapons in the middle stage and lasers in the close combat stage I believe.