All the beams have a use. They are more tactically limited than missiles, but they can be brutally effective if they are used correctly.
Nothing is better at jump point defense than beam armed vessels. A beam armed ship is going to fire several times before a missile armed can cycle through a flight of missiles. That damage can be telling. If your beam weapons are firing every 5 to 10 seconds, and the bad guys are only firing every 30 to 40 seconds, you can get in 3 to 8 shots unopposed. That can be telling in combat.
I have played through several games and have lost games to the "out of ammo" issue with missiles. Beam weapons give an excellent trade off, as long as you have the ship, they can fire, and generally fire fast. I try and find the best use for the guns depending on how the tech research at start goes. If I wind up with heavy tech investment in lasers, then the guns of the fleet are lasers. If I have heavy rail gun tech, then the guns of the fleet are rails.
Rail guns- Good basic PD weapon early on, as long as they are on a fast ship. Later (bigger) rail guns shoot fast and have decent hitting power, at higher tech levels, they can reach fairly far out there. Rail guns really work best on faster ships, so they can take advantage of the ship speed to target contacts. Railguns are also fairly cheap to research, making them a good option when funds and RP are tight.
Gauss- great PD weapon, and a VERY nasty fighter weapon for warp point defense pickets. Gauss fire incredibly fast, but have little hitting power and poor range. They make up for it in sheer volume of firepower and moderate weight. A squadron of 10 low tech fighters armed with Gauss can SHRED ships that have just transited into a system. Gauss can (should generally) be turreted, but fighters and smaller craft can make very good use of them. Research is cheap early on, but picks up quickly, making them most effective early to mid game.
Lasers- best range, reasonable fire rate, good hitting power and accuracy. Lasers are the defacto standard for beam weapons in the game due to being effective for both offensive and defensive uses. Lasers are the solid steady baseline for everything else. Later versions with size reduction can be mounted on fighters effectively. Only downside is the cost. Between focal sizes, capacitor, and frequency, lasers arent cheap in research points.
Plasma Carronade- slow firing, short ranged, and horrifyingly brutal pretty much sums up Plasmas. They are probably the most tactically limited of all the beam weapons, and really only shine in warp point defense. Strictly offensive, they are fairly cheap to research, since you only have to worry about bore size and capacitor, and they deliver very high damage. The down side is they are moderaly heavy, have slow refire until capacitor tech is pretty advanced.You can use them effectively in open fleet engagements, but it takes a VERY fast ship, and one with good anti-missile defense, or a pack of ships with dedicated AMM vessels.
Particle Beam- A pretty neglected weapon. Takes a lot of research, but can be remarkably nasty. Long range, and good hitting power at the higher levels. Couple to a fast ship with good fire control, this can be a pretty effective weapon, especially when you get strength 9.
Mesons- Very effective, but poor range. Good PD weapon vs armored missiles. Good fast attack weapon due to the skipping armor feature. Moderately expensive to research, they are a good all around beam weapon, especially since they can be used on PDC's, making them a nice standard beam that can be deployed on PDCs anywhere. Also can be mounted on fighters later on, making for a very dangerous combination.
Microwaves- very situational, similar to Plasma Carronades. Against targets with no EMP shielding, they are brutal. If the target HAS good shielding, they are horribly weak. If they work, you have a bunch of targets that cant defend themselves. If they dont work, you usually wind up with a bunch of dead fighters. Since they are so situational, they dont tend to get used very often by most folks. Since they dont do any physical damage, the ships that use them tend to be even more single functions specialized than most Aurora vessels.
I have run several games through a couple of versions of Aurora. My current game got me Plasma Carronades early on, and I used them very effectively on jump point defense ships, coupled with lasers. Once my capacitor technology came up, the carronades where very effective verses aliens jumping into my system with less than friendly intentions.
In my previous game, I got particle beam strength 9 from a ruin, and used it for beam armed capital ships. I also ran fast patrol squadrons of smaller frigate and destroyer armed vessels with dedicated AMM escorts, and the rest of the flotilla armed with gauss/laser combos, and several Particle Beam armed corvettes. They proved VERY effective vs smaller alien squadrons. The AMM/laser/gauss combo swatted the missiles till they ran out, while the particle beams savaged the alien ships. Since my smaller ships were faster, the NPR couldnt close with me to use their beams, and the missiles werent getting through the anti-missile screen effectively. In fact, my patrol squadrons were racking up more tonnage than my battle fleet and I could run almost eight patrol squadrons for the cost of one battle fleet.
Beams take more work, but they are worth it. I would never run a game with missile only boats again.