I actually find pvp more fun using my fed character. Why? Simply because in an Arena or a Capture and Hold the Klingon group tends to completely wipe out the other side without any effort (most of the time at least) while FvF and FvK on the fed side can really be a lot more challenging.
Its not just a matter of ships and of one side having better versions: the Klingons have generally more offensive oriented ships such as BoPs, battlecruisers and carriers that don't have a real fed counterpart, but lack in science ships and escorts. On average though it is more likely to find a better team while playing with the kdf (in PUGs) than with the federation and this also means you will win a lot more as a Klingon.
If you just want to win play Klingon, if you want challenge play fed. My advice is to try and pvp a little both your fed and klink toon and figure out what you prefer: if you love BoPs then you HAVE to play klingon...
And yes, FvF queues are a little faster than FvK because there are a lot more players there.
Both sides have their advantages and disadvantages, as it should be. Federation has strong escorts, a science ship line to pick from, cruisers that are more oriented towards healing/tanking, and even have 1-2 carriers to pick from.
KDF has somewhat more attack-oriented ship models. BoPs are great harassers and sci-spammers, raptors are okay offensive ships though they're not quite as good as Federation escorts, and battlecruisers can both tank and DPS quite well in the right hands. KDF also has the edge in carriers, which can do a reasonably good job in the support-team role if needed (especially the Vo'quv). What KDF doesn't have is a good selection of science ships, and the disadvantage in escort-level ships.
On the face of it, one could say the KDF has a slight advantage in PvP. It depends on how you look at it, and player skill can change many things. A good Fed team comprised of a sci ship, 1-2 cruisers or carriers, and 2-3 escorts can do a pretty good job at fighting. . .it's a well-balanced team, something the KDF has trouble accomplishing sometimes.
I prefer KDF, but I'm probably biased by my KDF fanboyism
Which faction is currently doing the best at PVP, in general? I've got a KDF up to 50, but in the limited time I've played him, KDF seems to dominate the queues. Was my experience typical?
Also, are queue times any quicker for Fed?
The best PVP players are Klingons, by far. They coordinate better, they know how to fit their ships, and on the few times I've been moved to the Klink team in Ker'rat, and allowed to open fire on my fellow Feddies... I feel like I'm Jet Li fighting a guy in a wheelchair.