Okay to start out. I don't want tot see an exact copy of the Klingon carrier over on the fed side, instead I would love to see a pet class ship, maybe using drones, and some other cool concepts that could lay off of that.
now time to get to the nit picking (and I hope I don't offend anyone, just pointing out a few flawed arguments to set the record straight.)
first off to the guy who said that star fleet has never made, nor will make a battle ship. I give you prime example a: The Excelsior. the Excelsior was classified as a Star Fleets battle ship during the TMP era. It brought the heavy fire power that Star fleet needed to fight wars to the battle front and was able to move around and defend federation territory from any threat that it would see. While the only carrier we have seen on screen is the Akira, I like it's role as a torpedo destroyer.
Secondly, as to the cloak. The real reason star fleet never got a cloak is becasue the creator, Gene Roddenberry said "Good guys don't sneak around." which while true from a dramatic point of view, lets take a look at how this has really cemented the federation into an all or nothing sort of scenario. While the Klingon use cloaks to sneak attack the enemy, the federation could have used it to sneak into contested territory, investigate claims of, lets say illegal weapon research, and get out of there. Instead, (in the the shows) they have to negotiate to get access to investigate, and if they did something wrong it would come down to a fight. IN a game it basically translates into this. You are given the mission to investigate a facility rumored to be a weapons testing facility. You show up, upset the inhabitants, fight your way through countless ships just to get to the facility and investigate. Best case scenario, you were right, and those people you just obliterated were in the wrong, worst case scenario, you were wrong, just attacked an innocent civilization and maybe provoked a war.
Of course any peace loving organization would instead spend all it's time trying to negotiate with their enemy to have them release the data of the facility and take no action if they refused, just like our U.N.
Which brings me to my next point. The federation isn't like the U.N. It's more like what the U.N. should have been. An organization design to organize the many governments under their umbrella and give a unified set of rules to live by. They also have their Star Fleet which is a military/exploratory branch of their organization, which has the authority to act as they see fit under the guidelines of the Prime Directive.
Our U.N. can hardly get any of the governments to agree to anything, and any time they send in troops, it's with the explicit orders to never open fire, unless you wanted to tried for treason. Sadly, this also includes when the enemy is shooting at them. watch hotel Rwanda, which is based off a true story. Look at how the U.N. handled the claims the Iraq had nuclear arms. Despite the fact that Iraq was required under treaty to submit to an investigation on their nuclear plants every so often, Iraq actually denied the U.N. for over six months to even allow investigators in, much less surrender any information. More to the point any time a major conflict erupts around the world, it's not the U.N. forces that intervene, it the U.S. forces that are required to step in, becasue unlike the U.N., the U.S. at least has the balls to get the job done. The U.S. has been on many occasions been chastise for not intervening in massacres becasue we wanted to stay out of them as a matter of public approval by the U.N.
So if the Federation acts like the U.N., then ther eis no way that the Klingons would have had to sign the Kitomer Accords in the first place, and the Romulans would be walking all over Federtaion space, becasue Kirk And Picard would be under orders to not do anything as all the nations sit around and argue about what to do for years on end. In fact, not only would the founding planets be part of the Talks but the Klngons, Romulans, Cardassians, Dominion, and any other Race would have equal say in the affairs of the Federation, and dead lock any executive decisions the Federation ever came up with.
Luckily for us, the Federation is run as a peace loving Galactic Government that does carry a big stick around. They do get things done, with only a few set backs. And when they do go to war, which is often, their military is capable, fleshed out, and after all the blood shed, the Federtaion goes above and beyond and starts to help their enemies rebuild into a better, more peaceful empire, that can coexist with the Federation.
So, while Star Fleet would certainly have carriers (assuming fighters are really that effective) they Have, and Probably still do have Battleships. But with almost all federation ships, they serve a secondary purpose of exploration and patrol. While cloaks would make tactical sense for all races, I think only the war like races should have battle cloaks. The Federation use their for recon and special operations, but would decloak and stay decloaked during a fire fight and engagement.
As much as they are a "righteous" peace loving society. They must also be militarily viable an entity. After all, they want to be around after the fight does occur, and while they would try to avoid conflict, they are by no means afraid of it. And unlike our lovely U.N. who is at this moment trying to disarm not only citizens across the world, but also military powers, becasue they feel that a peaceful society is one where they don't allow conflicts (A.K.A. people will die in senseless blood sheds all around the world, but becasue the U.N. refuse to acknowledge it, as there would be no way such crimes would happen with out guns in innocent peoples hands.

(and yes I am being condescending to the U.N. becasue this is there personal view on violence through to world.))
As far as Feds getting carrier in STO, we don't need the same ones the Klingons do. Let them have the "Carrier", and give the Federation a drone frigate, or something in which we can summon our own pets that can do different things. Just make them comparable.