The Q most often arises in full tech games. That is, how should one arm ships if one has all the weapons' tech?
A similar Q arises in what defenses, if any, should one put on ships in full tech games.
For example, in one recent game, I was at war with two strong AIs at the same time. Their worlds (and hence, fleets) were intermixed. Both used beams, but one had armor and the other had shields. My expeditionary force would almost certainly have to fight both and, so, obviously should use missiles. However, should I avoid defenses, since they would face two different weapon types, perhaps even on the same or consecutive turns? One thing seems clear, and that is that it is better in full tech battles to have no defense than the wrong defense. That is, the space and cost used for wrong defense would be better spent on weapons.
One thing I did was to actively placate the third strong AI, mainly because it used missiles and missile defense!
A few posters have lamented that late game wars, when multiple parties have essentially all the tech, are boring because design details no longer matter. That is, they have felt that it came down not to design but economics, in that it mattered not how the ships were designed, just how many one had gotten to the battlespace. There's certainly an element of truth there, but that complaint does not really match my experience. Adding some high defense ships to fleets (the "right" defense) seems to consistently let me win those fleet battles and preserve some ships.
Yet, even the economics approach is not without interest. That is, if one presumes one has a certain # of BCs to make a fleet, what should the fleet makeup be? In SEIV, that was a favorite theme for set piece battles. Another theme included also a set number of research points used to get the hardware, but this would not be relevant for a full tech premise. In the research points one, for example, do you allocate points to get the largest hull? Reinforced? What about that research trade good improvement? Invest in defenses? In a research points battle, the psyonic beams would always seem to win, but one would get a different result if one used only BCs, because the psyonic beams are more expensive than the beam weapons much later the research tree.
So, with strict economics, and assuming no red bases or racial points, would a (say) 50 logistics point fleet be better with all small hulls? What about some small hulls, a few cargo shooters, and a couple high defense huge hulled dreanoughts? Or, maybe just five 10 logistic points dreadnoughts?
The economics Q becomes relevant if one is resource limited. A similar Q becomes relevant if one has, say, 20 planets local to the battlespace. The more expensive ships take longer to build, and there are some limits to what one can just purchase. What mix does one build? The smaller/cheaper ships can join the fleet one per turn or every other turn. The big ones might take 10 turns or more.