It should first be said that the metagame always has the ability to change at any given time. Several factors impact this heavily, namely success found in tournaments by the competitive professional teams.
As seen at IEM Hannover, the meta game between the three regions is essentially the same. All of them utilize AP mid, ranged AD with support bot, jungler, and either a bruiser top or AP, depending on what team comp they were going for and counterpicking. This has effectively been the metagame in all regions, and until someone comes with a different metagame that does well against it in a tournament setting, it will likely stay.
Prior to Dreamhack, the NA meta (can't say US only, since many players from Canada play, for instance of several members of CLG and TSM are Canadian citizens - at WCG: ChaoX, TheOddOne, HotshotGG, BigFatLP, and Elementz represented Canada) ran quite differently to EU. NA teams at the competitive level ran a tank top, jungle, AP mid, ranged and support bot, while EU teams ran double AP in solo lanes, jungle, ranged and support bot. The casual games on NA was still running, double tank lanes bot, AD carry mid, AP top with jungle, and many games had no jungler. I know this because this is when I started playing LoL heavily. At Dreamhack, it showed that EU was more used to AD with support bot, and great plays were made continually by their bot lanes. The eventual winner of course was fNatic led by xPeke and Shuushei showing off their double AP comp to quickly burst the enemy team with AoE damage and making it easy pickings for their AD to finish everything off.
Flash forward to IEM GamesCom, the NA teams now having chance to get more practice with the AD/support bot lanes and think of ways to counter the double AP strategy. NA teams, come up with tanky DPS top and tanky DPS jungle giving way to the Bruiser meta. In one game of TSM against an EU team I cannot remember, TSM takes Soraka/Jax bot lane to combat the Urgot who had given them problems the game before. They had three bruisers and managed to pull off the win before falling to CLG in the finals where the first two games was playing protect the KogMaw.
To answer your question then, it wasn't really a matter of teams playing different metagames, however they understand what counters what and know how to play accordingly. Double AP gets countered by a bruiser/tanky DPS comp. AoE team comps can win teamfights but can be slaughtered to a poke comp where they don't allow a teamfight to happen before they poke you down too much, a push comp counters a poke comp. So counterpicking, and strategies to execute is used a lot to help gain the advantage. For instance, picking a very strong late game comp against an early game team comp and playing super passive to stall the game. Nasus, Irelia, Karthus, Vayne, KogMaw are examples of champions that have an insane lategame but an early game that can be shut down (not so much in the case of pre-nerf Irelia). On the other hand, Urgot, Ezreal, LeBlanc, Alistar, Udyr start to fall off heavily in the late game compared to their counterparts unless they have built up a big item advantage.
As for everyone knowing and following the meta, it can be both a benefit and negative depending on what side you take. In many tournaments, teams have picked like they were following the meta, but in game swap lanes to give themselves the advantage. This is most common with top and bot lanes switching. It also happens with mid lane and top lane as most players use their runes to give themselves a laning advantage. For example, let's say one team's top and mid are Malphite and Galio respectively. The enemy uses Riven and Karthus. Malphite thinking they will face Riven, choose to use a full armor page to effectively negate most of Riven's harass combined with Malphite's passive. Galio similarly use full magic resist page to negate anything Karthus can do in lane. Lane starts and you find they swapped on you. The difference is they could have chosen to rune for it or not, but either way, Malphite and Galio is at a disadvantage since their runes do little for them. Sure Malphite's damage builds with armor and Galio gets more AP with magic resist, but they aren't going to have much fun in the lanes. To compensate, they try to quickly switch. But the enemy team can switch as well, forcing another switch or unfavorable matchup. Each time you switch lanes though, one of your lanes will tend to fall behind, and since you made the first switch, your team will lose out allowing the other team to gain an advantage.
Best Answer
In extreme brief:
And now, the "TS;DR" version ;-):
Source, from which I paraphrase extensively.
There are three cases worth considering (all other cases are some amalgam of these):
The goal of the matchmaking system is to find what is approximately the team's Elo and find a team with a comparable Elo. That translates into having a 50-50 chance of either team winning. The longer you're in queue, the greater the difference between two teams' approximate Elo is allowed, thus the greater difference in your estimated percentage chance to win.
At the root of the question is how that number is determined.
In the root-case of everyone being in solo-queue, in any game type, the system first locates other people approximately your same Elo then loads you all into a team and averages the Elo of each member. Once it has two teams "in queue" with approximately the same team Elo, it will match them into a game.
On the other extreme, if you're a 5-man pre-made team, the same process is followed except the team is already full (so it doesn't need to locate other players for the team), and the team Elo gets a small bonus (described below). In ranked games, you will only be matched against another 5-man pre-made team. In normal games, I believe (and ought be corrected or confirmed with an edit and source citation) that 5-man pre-made teams are preferred but you don't necessarily get matched with one.
In the middle, things are slightly more complicated. Once you enter a queue with teammates, everyone's Elo is adjusted to be the same value. That value is the average of everyone's Elo plus, again, a bonus depending on several factors (again, see below). Once you're all in the pool of active game-seekers, it locates other players who have approximately the same Elo as your adjusted Elo. Obviously, when it examines another player's Elo it could be looking at their adjusted Elo, too, in the case that you have a team of 3 and a team of 2 being put on the same team of 5. Once it has created a full team of five, it does a final averaging of the Elo everyone entered the team time (adjusted or not). That final averaging is your team's Elo. It then locates another team with the same team Elo and BAM: puts you in a game.
The question now is what kind of bonuses you get. Riot won't release the exact values, and there are a number of cases to consider. I'll let the a different source do the talking:
Finally, with all of that information, we can address the question of "Isn't matchmaking somehow unbalanced?"
"Unbalanced" we can safely take to mean that it grants advantages to one team or person over another. Since virtually any "person" advantage is also a "team" advantage (you don't gain or lose Elo individually; only as a whole team) I think it's safe to say we don't need to cover them individually. One assumption I am making is that Elo is a fair approximation for skill. Disagree all you like, but some assumption of the system's validity needs to be made in order to discuss it.
Riot obviously has gone through significant effort to make sure that the system is difficult to abuse. I also won't speculate on measures we're not fully aware of (Newbie Island and abuse detection). However, two people of inordinate skill differential (say, 0 and 1800) would end up at 900 + some arbitrary bonus if they queue'd together. If you have three people at 0 and one 1800, you would get 450 + some (larger) bonus. An 1800 Elo player can generally be expected to carry a 450 Elo game and a 0 Elo player is unlikely going to be able to throw it. In this sense, the system as presented can be abused.
If we take a more realistic case, however, of an 1800 Elo player helping a 1200 Elo player (let's say their Elo has stabilized; I know you get significant (40+) Elo gains and losses early on), the difference is less pronounced. That would put them at 1500 Elo, plus a bonus, which a 1200 Elo player can certainly throw due to the ability of the 1500 Elo players to take advantage of their mistakes (something that 450 Elo players have a harder time doing). However, the 1800 Elo player is going to have a harder time carrying the game alone.
You can see that, even without extra knowledge of the system, it's hard to make the situation measurably "unbalanced" for the majority of cases.