The change from Bond wearing a Rolex appears to have been for two reasons--one stylistic, the other financial.

Foremost, for introducing Pierce Brosnan as the "new" James Bond in the 1995 film GoldenEye, the producers wanted to update the image of Bond to a more distinctly sophisticated "Euro" look. Lindy Hemming, the costume designer for the first three of the Pierce Brosnan appearances as Bond was quoted in The European Magazine ["The Names Bond, Euro Bond", July 7-13 1995] as explaining: "Sean Connery wore a Rolex, but we thought they'd become a bit ordinary now. OMEGA are more minimal--even though this one does shoot off a bomb."

She is not alone in thinking this. Rolex as a brand has changed a lot since the late 1950's when Fleming chose one for Bond to wear. At that time, Rolex was known as a uniquely well made, durable and "waterproof" watch that cost somewhat more than other watches. Now, decades later, many inexpensive watches meet the functional needs of durability, accuracy, and water-resistance that people used to turn to Rolex for. In this time, Rolex has shifted from being a technically superior, but only modestly well known watch make to being the publicly perceived "leader of the pack" in the luxury watch market.

Because of this, many Bond afficionados believe that the OMEGA Seamaster is closer in spirit to what Fleming would choose for Bond today. The literary Bond would not have chosen a watch based on luxury and flashy name recognition, but on performance. To him, any watch, car, or other implement's primary function is as a tool. Any tool is expendable. The Seamaster offers the comparable performance, style, and weight Bond would have wanted, but without attracting extra attention or making the statement a Rolex does today. With OMEGA's much heavier bracelet on the Seamaster, it would probably make an even better "knuckle duster" as the literary Bond once used his Rolex in a fight.

The other reason is that with all the product marketing deals that surrounded such modern high-profile films, the filmmakers wanted to work with a company that was interested in high-profile co-promotions--something that Rolex conservatively avoids. Reports are that the film producers chose OMEGA as their leading candidate as a replacement for the classic Bond watch, then contacted OMEGA to ask their participation in providing products and being involved in co-marketing arrangements.
http://www.chronocentric.com/omega/bond.shtml(source)

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