If you get the Piccadilly Line Tube from T4 you go direct to South Kensington for various museums, Holborn where you can walk to the British Museum or Kings Cross for the British Library.

Whereas taking the HEX for anywhere except the immediate area around Paddington means getting a Tube / Bus / Taxi

If you change at Hammersmith or Earls Court BTW (walk across platform) you can easily reach Trafalgar Square / Westminster Abbey / House of Parliament / Big Ben / St Pauls / Tate Modern / Tower of London

AND it's also a LOT cheaper