An exclusive game title doesn't necessarily define a console brand, especially if you look at the 2 biggest competitors, the Xbox 360 & The Playstation 3.

The Xbox 360 has more exclusive titles while the Playstation 3 has more exclusive franchises. According to an interesting article at the Startscreen.com.

"The biggest disaster this generation is having an exclusive title and then seeing its sequels end up on multiplatform consoles. We have been seeing too many titles jump ship. Both the Playstation 3 and the Xbox 360 have been victims to it. How many perceived exclusives were lost on these consoles by going multiplatform?
The Playstation 3 suffered their losses most notably in the beginning of its lifecycle. Big names like Final Fantasy and Grand Theft Auto were looked at as a Playstation brand. In recent times, however, the Xbox 360 has been suffering a similar fate. 2 years ago titles such as Bioshock and Lost Planet were considered Microsoft’s bread and butter. Bioshock jumped ship completely while Lost Planet jumped over as a sequel onto the Playstation 3.
In the aftermath of it all, we look at what's left," according to the he Startscreen.com editor.

The editor of Startscreen.com came to the conclusion "The Playstation as a brand remains strong due to Sony’s well established game library both past and present. They’ve had more time and more in-house studios to accomplish that task. The same can’t be said for Microsoft though. It seems they have taken another route to focus on their Xbox Live service and securing downloadable content instead of building up their own library.
As you can see the Playstation 3 excels at exclusive franchises. On the flipside the Xbox 360 excels at obtaining exclusive titles and downloadable content. These are the two main differences that define these console brands."

You can read the complete article here.