The retailer is offering the first person to spot a difference between the two spots a chance to win a hamper, claiming that the two ads feature Santa's visit to a sleeping household, subdued lighting, the same soothing female voiceover, fireplace, mince pies, and a child tucked up in bed.
Crucially, the two ads both use same style of onscreen captioning as the camera drifts around the family house.
Christian Cull, spokesman for Waitrose, said: "The camera shots are similar, the movements are similar, the subjects are similar, the story is similar and even the featured products are similar."
The company has offered Woolworths the chance to preview its next Christmas ad campaign so it can prepare a similar version.
The 2002 Waitrose campaign was created by Banks Hoggins O'Shea, which is the John Lewis Partnership-owned supermarket group's retained advertising agency.
Woolworths admitted that there were similarities in the ad, but said that it was just one of a seven-part, eight-week series of ads to push Christmas sales.
Mark Trinder, head of brand communications at Woolworths, said that the Woolworths ads were not price pointed, unlike the Waitrose spots, and that the range of products went across the whole Woolworths offering while the Waitrose ads promoted only food.
"I think that there are similarities, but in retail marketing there is always a lot of work that is similar," Trinder said. "I wouldn't say that anyone is copying or mimicking."
Woolworths appointed BBH to the account in April last year after 17 years with Bates, which subsequently closed after further losses.
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