Although the Yeomen of the Guard is older, the Gentlemen at Arms are more senior, due to their being classed as 'gentlemen' rather than 'yeomen', and because they are classed as the 'nearest guard', i.e. the personal guard to the Sovereign. The Royal Company of Archers performs this role when the Sovereign is in Scotland.
Other Royal Bodyguards
Yeomen Warders were originally a detachment of the Yeoman of the Guard, appointed by Henry VIII to guard the Royal Palace of the Tower of London in 1509