What are the differences between 5vs5 and 3vs3 in League of Legends?

Solution 1:

A major difference between 5s and 3s is how much lane control you need to win the game. To summarize: for 3s you want high dps champions with a lesser focus on team value, and in 5s you want high lane control champions with great team value.

In 5s you value champions that can hold their own lane well, because teammates will leave their lane open for minutes while they travel to help you. In 3s you value champions that can help other lanes and contribute lots to ganking, because traveling lane to lane takes very little time.

Champions like Heimerdinger and Soraka do well in 5s because they both have great lane control. Heimerdinger's turrets and passive heal allows him to push a lane very well and stay in good shape, meaning he doesn't need to leave the lane for a heal and spend a minute running back out. Soraka can heal herself and replenish mana, so she almost never needs to leave a lane.

However, in 3s they are less handy because they are squishy and susceptible to being ganked. They also provide little value when it comes to ganking in other lanes because they are not damage-per-second champions. To contrast Heimerdinger and Soraka, Tryndamere is a champion who shines in 3s. He can quickly travel from one lane to another by spinning over walls, and his dps makes ganks easy.

Another thing to note is that you require team composition in 5s, as any one champion can be focused down by 5 others at a time without a team backing them up. In 3s it's less of a problem because champions last longer in team fights as less damage is going around. Tryndamere in 5s can be crowd controlled by 5 other champions and he provides no aid to his teammates. However, in 3s he can solo two champions and likely win.

Solution 2:

From what I've seen, 3v3s are much more focused on teamwork and ganks. As Twisted Treeline only has 2 lanes for 3 people, most matches start with a random decision based on which side will have 2. It's also much more likely that there will be teams starting with all 3 in one lane for a quick kill/tower attack. In this regard, I consider 3v3s extremely chaotic; a lot of the match is decided based on who is where and at what time. Teams are also much more likely to travel together on ganking runs.

I vastly prefer 5v5s, but it comes down to my character preference. Since I main Heimerdinger, I benefit in long, drawn out combat so I can annoy with my ranged attacks and run. In a 3v3, Heimer proves too fluffy and susceptible to getting killed extremely quickly. Physical/melee champions seem to thrive in 3v3s more than ranged dps champions, so it may come down to who you like playing. Try both out and figure out your preference.