I don't think Phillips is better than Rice at progressing the ball like that.
It's just a general weakness in England's midfield and what they have available. Bellingham and Rice are great at progressing the ball with carries, but when one has to play as the pivot and progress it with passing, they can't do it. There's no-one available who can from what I see. One of the problems they've had for years, probably since Carrick, that other teams don't suffer from. They need a Rodri/Tchouaméni/Jorginho/Enzo Fernandez type. Or even a different type of number 6/8 that can do it - Verratti, Pedri, Modric etc.