Why did Roald Amundsen's party beat Scott and his men?

Largely because Scott was relying on an unproved strategy involving the use of not only dogs (as Amundsen did) but also horses and motor sledges for transportation. As it turns out, neither the horses nor the motor sledges performed nearly as well as Scott had hoped.

It's also worth noting that Amundsen's party set forth nearly two weeks before Scott's did (October 19 vs. November 1), though this was not the only cause, since Amundsen beat Scott to the pole by the considerably wider margin of five weeks (December 14 vs. January 17).