I think the difference between Paul McCartney's family and the Beckhams, his daughters may be famous now, one through photography, like her mother. Stella is a well known fashion designer and graduated from Central St Marin's in London and whilst the McCartney name almost certainly helped elevate her to where she is now, she has at least credentials in that field. McCartney's children's growing up years were away from the limelight and they were educated in the state system.
Victoria Beckham is lauded as a fashion designer without any training, she allegedly has the ideas but I imagine has a gamut of people working for her who do the actual designing cutting and marketing. Maybe she shouldn't bother though, since it's inception her business has lost £56,000,000 DB has constantly dug into his coffers to prop it up and although she often tells her public how hard she works, working that hard to make such a colossal loss seems a bit pointless!