I think William and Henry complement each other well. The fact is that if you like "traditional" names (and I do) then the chances are they will have been used by the royal family at some point as they also use traditional names.
The Royals have used James, William, Henry, Victoria, Elizabeth, Charles, Catherine, etc etc which all 'go' well with henry as they are names in the same vein.
George William Charles Frederick Thomas Alexander Arthur Edward James Oliver Ambrose Asa Caleb Caspian Clement Peter Raphael Robin Conrad Cyrus Silas Dominic Eli Frances Jasper Franklin Monty Rowan Albert Joseph Hugo Samuel Leo Oscar Theodore Benjamin Patrick Tobias or Toby Rupert Sebastian Wilfred Alistair Arlo Digby Nicholas Angus Benedict Christopher
Florence Matilda Alice Honor Elizabeth Sophie Charlotte Isla Isobel Annabel Beatrice Jessica Martha Rose Willa Susannah Serena Miranda Miriam Pearl Gabriella Flora Sophia Cecilia Clara Lara Imogen Lucy Tabitha Alexandra Eliza Emma Allegra Arabella Eve Phoebe Elodie Frances Laura Zara