The Amulet of glory has the same Attack bonuses as the Amulet of fury, is far less expensive, and, unlike the fury, has the ability to teleport to several locations, but the Amulet of glory has lower defence, strength, and prayer bonuses than the fury.
If the Amulet of glory has any charges, wearing it while Mining will increase the chances of finding gems. Wearing it when mining the Shilo Village gem rocks will also increase the speed at which gems are mined.
At level 47 Construction, the Amulet of glory can be mounted in a Player-owned house, within the Quest Hall. This will require an uncharged Amulet of glory, and 3 Teak planks. While mounted, this amulet can be used to provide unlimited teleports.
Amulets of glory are also useful for Runecrafting through the Abyss, granting a fast way to return to Edgeville. In addition to that, the amulets can be used for runecrafting Law runes by taking the boat to Entrana, then teleporting to Draynor Village to bank the runes.
In conclusion the amulet of glory has more uses but is slightly weaker, me personally i have the glory because of the reason provided above.