The Apple v Apple case in the UK hinges on the court's interpretation of a latent ambiguity in the original agreement between the two companies.
Apple Computer were allowed to use their logo for "...computer software of any kind on any medium..." and "data processing services, data transmission services..." and "ancillary services relating to... distribution."
The Beatles Apple label are allowed to exlusively cover "any current or future creative works whose principal content is music and/or musical performances; regardless of the means by which those works are recorded, or communicated, whether tangible or intangible"
So they both have a justifiable claim. It's just that a service like iTunes wasn't anticipated when the two sets of lawyers hammered out an agreement circa 1991. It will be interesting to see which way the judgement falls.