The first striking difference between how Prince William intends to fill the role of Prince of Wales and how his father did so, is that William does not plan on having an elaborate investiture ceremony to accept the role (via The Mirror). An unnamed royal source tells The Mirror that William has "no plans for any kind of an investiture like the Prince's father had." Further, this source explained that William and Catherine, the Prince and Princess of Wales, are "focussed on deepening the trust and respect of the people of Wales over time."
Another significant difference between William and his father will be that William and Kate have chosen to have a significantly smaller staff serving them. In fact, The Sun reports that the royal couple will have a staff roughly half the size of their predecessors in order to "create a more cost-effective and less formal team." Prince William has also reportedly told his staff that they don't need to wear suits to the office in order to create a "less stuffy" environment.
Further, in order to modernize their roles, William and Catherine are said to have done away with the "never complain, never explain" protocol, which was long-held by royals before them, thereby making themselves seem more accessible and forthcoming to their public.