It's really quite simple. It's got nothing to do with us favoring it over the PlayStation 3—as a matter of fact—it is because we've never really even considered the PlayStation 3 to be a video-game console. Sony even marketed the PlayStation 3 as a Home Entertainment and Media System. Well, basically, that's just a fancy way of saying game console, but the truth is that the PlayStation 3 has always been more like a personal computer than an actual game console. First of all, when it launched it came with the option of installing "Other OS", which means you could have Linux running on your PlayStation 3. Most mice and keyboards were also fully compatible with the PlayStation 3 meaning that it was often as easy as plug and play. Let us not forget to mention that the PlayStation 3 was also the cheapest Blu-ray player and wireless media server. I know a lot of people who merely own a PlayStation 3 because it is a brilliant media server: games are just a bonus for them.
It's an actual gaming console
The Xbox 360, on the other hand, is the ultimate gaming console because it was built for one purpose only; to game. The Dashboard (Xbox 360's OS) is the most efficient gaming operating system today. You have full access to all of its features even whilst you are in the middle of a game. It's quick, easy, and very effective. Whether you want to join a party, send a video or audio message to a friend, or even directly chat to another friend who is playing a completely different game you can do so with a press of a few buttons without it hindering the performance of the game. This is definitely not news to a lot of gamers, but it is certainly one thing that is overlooked when comparing gaming consoles—and yes, even the PlayStation 3. After 6 years the PlayStation 3 cannot do Cross-Game chat, and it is because of its operating system, XMB. Sony used the XMB differently. You can watch flash videos on your games web-browser. Nearly all video-files are compatible and will play on the PlayStation 3. It also includes an automata media-server and is easy as pie to set-up—but that's no good for gaming.
The Xbox 360 controller is designed with the gamer in mind. Though my personal presence is, of course, the PlayStation 3 controller, there is no arguing that Xbox 360 controller is just a much better controller for hardcore gaming, with the exception of fighters; PlayStation controller wins there because of it's multi-button layout for the d-pad. Because there is no indent for your thumb on both of the PlayStation 3's analog sticks my thumbs often slip off and I usually end up with sore or bruised thumbs the following day. The Xbox 360's analog sticks are indented which means my finger, if ever, barely slip off and it is also not as stiff when you press them in. The trigger buttons are also a lot more accessible when playing shooter games. You have a more firm grip on the controller and your trigger finger is in a more comfortable position meaning popping head-shots in Call of Duty or Battlefield is a cinch.
The Xbox 360 gives you a sense of identify when playing online. You can spend hours on end creating and tweaking your avatar until you've perfectly content with what it. Your avatar is then used as your mascot in a lot of Xbox 360 games. It also serves the purpose of giving your profile some style in giving you a sense of identity within the community.
Nothing tops the Xbox 360 community. You'd struggle to find a game where there is no one on microphone chat. Also, the community is always kept up to date with fresh community exclusive content such as news casts and contests, and the community managers always to a top-notch job in getting everyone involved.
Now that I've pointed out all these wonderful things that make the Xbox 360 the ultimate gaming console, I am going to hit you with a M. Night Shyamalan twist... I sold my Xbox 360 one year ago.
The Kinect was the real killer for me. Before the Kinect, the Xbox 360 was all about hardcore gaming. It was where all the dedicated gamers would play. I miss al those long nights of Call of Duty or Halo online fragfests. Partying up with my friends and jumping straight into a lobby full of eager gamers ready to have some fun. Though I cannot really say that much has changed and I could still play some classic Halo 3 or Call of Duty 4 with my friends on the Xbox 360, I just couldn't justify keeping the console when I already had one console built for casual games that already had me waving my arms around like a weirdo, and a home entertainment system that played most of the games that were already available on the Xbox 360, and for free. After the Kinect I sort felt abandoned by Microsoft... kind of like they had lost their way and weren't certain on the path they wanted to take. The E3 exclusive announcements for the Xbox 360 in the past two years have been an absolute joke. The PlayStation 3 was more than enough, besides, the exclusives coming out look innovative, quality, and fun.
So, there you have it. Xbox 360 is a definite winner when it comes to being a standalone console for the sole purpose of gaming. The PlayStation 3 serves more purposes and is certainly of more use in my apartment; blu-ray player, media-server, Internet Browser, so on and so forth... but damn do I miss gaming on my Xbox 360.