Most people would notice that the United Federation of Planets fields very powerful ships - the Galor class Cardassian ship and the Klingon Bird of Prey, though staples of their respective fleets, would seem to be at a serious disadvantage in a one-on-one with many of the Federation vessels we know about.
We know that the Federation has better sensors than the massive Warbirds of the Romulan Empire, but that even they are very often seen travelling in pairs - Federation ships, however, are generally alone.
However, when the Federation does have to potentially combat these fleets, they are often portrayed as seriously outnumbered. This numerical handicap suggests that we aren't just seeing the Federation's finest vessels, but that they are building fewer and better ships than civilizations that may pose a threat to them.
This is all despite that fact that those civilizations are just as intelligent and usually have access to (on average) comparable technology.
This seems like a huge combat disadvantage. As we know from nature, K-strategist species (species that reproduce slowly and invest much in new members which are usually intelligent: elephants, for example) are badly outnumbered in both type and count by R-strategist species (species which produce many offspring and refuse to care for them - fruit flies, for example.)
But there is a further reason for that: vessels of all kinds have what is called an exponential problem curve, meaning the more problems it already has, the faster it gets worse. For example, if shields are weakened, engines are far more likely to become weakened quickly, and vice versa. If life support is damaged it may hinder repair efforts: so on and so forth. In other words, the more problems a ship has, the more likely it is to get more - non-linearly, in fact. (And I read about this in a real book on Naval warfare.)
Thus, if a mighty Galaxy class ship is fighting three Klingon Birds-of-Prey, and he damages one, he still has to start two more firing enemy vessels down the slippery slope of their exponential problem curve. If the Galaxy class suffers one lucky hit, however, the battle is almost already lost.
Worse, I would have to guess that adding fire-power would be much cheaper than adding a Science Suite (though I'm not sure.) I.e, perhaps a few small specialized warships are a more efficient use of resources, for combat, than a few large ships with many extra features?
Therefore, my question remains: is the Federation actually much weaker than the other major powers? Are there non-idealistic reasons for the Federation choosing this quality-over-quantity strategy? Its vessels could easily turn a close battle between weaker kinds of ships, but could it even defend itself on its own?