The PlayStation 3 and the Xbox 360 are both great systems. Being a fan of both, I know how they work pretty well

Before I start I want to let you know that personally, I am an Xbox fan, simply due to the fact that the multiplayer servers are way better than PSN servers. So let's get started there. Xbox One and Xbox 360 have great internet connections. Although Xbox Live costs money while PSN doesn't, there is a reason. PSN (PlayStation Network) has bad connections most of the time. You will often lose connection to the host or lag out of a game. If you've ever played the game Contagion on computer, one of the things it says when the game starts up is the phrase, "frag, not lag" It's basically saying their servers will not lag and you can get kills. This is true and applies to all systems or devices. PSN however does not meet that (once again, most of the time). Xbox Live on the other hand runs on really expensive servers and needs the money to run them. If Xbox Live was free, the servers wouldn't be as good.
Winner: Xbox 360

Now, let's move onto graphics, as that really helps with the style of the game, it's obvious PS3 has better graphics. Unfortunately, Sony neglects to share anything with Xbox (except the Interview). Because of this, Xbox cannot use Blu-Ray, which belongs to Sony. Instead they have to use DVDs. So if you're ever wondering which has better graphics, there you go.
Winner: PlayStation

When both systems were released, they costed a lot more than they do today. They had ups and downs simply based on what they could do for the cost. According to this article on pcmag.com, it is basically a tie:

The Xbox 360 has a very slight advantage at the low end, with a $199.99 bundle that includes 4GB of storage and a wireless controller. The Xbox 360 Elite with 250GB of storage rings up at $299.99. If you like to play motion-controlled games, a $299.99 (4GB) or $399.99 (250GB) bundle adds a Kinect sensor. Meanwhile, the Sony PlayStation 3 with 160GB of storage is available for $249. A bundle with a 320GB PS3 and Sony's motion-control add-on, PlayStation Move, will cost you $349. The $200 Xbox 360 is the least-expensive entry, but if you want your game console to double as an entertainment system, the $250 PlayStation 3 with 40 times the storage and a built-in Blu-ray player is a better bet for the money.

So to determine the winner for price, it must be separated into two different sections. For the best entertainment system, the PlayStation 3 wins. For the best gaming system, Xbox 360 wins.

Moving on to, exclusive games. PlayStation 3 has many exclusive games that are amazing. Xbox on the other hand has about one. The PS3 features the Last of Us, one of my favorite exclusives, Killzone, another one of my favorites, Uncharted, and many, many more. Xbox features one masterpiece of a game: Halo. Because there's only one exclusive game for Xbox 360 (that I know of), I'm going to give a description. Halo has 5 games released and one coming out soon (Halo 5). Halo 1-3 follows Master Chief, a super soldier who is going to save the Galaxy from the Covenant, an evil alien race. Halo 4-5 also follows him. Halo 3:ODST and Halo: Reach follows two separate people. The Last of Us, Uncharted, and Killzone have really long stories in which I have not finished, therefore I'm not going to explain the entire story. Uncharted is about going after treasures, The Last of Us is about a fungus that turns people into zombie-like creatures, and Killzone, is close to the same story as Halo. An alien race, the Helghast, invade Earth and we must fight them off.

Overall they are both amazing consoles for different things. The PS3 is great for entertainment (movies, TV shows, etc.) while Xbox 360 is good for gaming. This should settle the debate down a little bit.

Entertainment ratings:

PS3 -10/10
Xbox 360 - 6/10

Gaming ratings:

PS3 - 7/10
Xbox 360 - 10/10