Swift Anklet is the best favor item.
Why do people get anything else?
Barring really exploitative combos like five Heaven's Wrath to focus on a single demigod or something, I do not see why people get anything other than Swift Anklet as favor items.
Speed is probably the single most important stat in the game. With it, you are able to chase down enemy demigods, you are able to run away from enemy demigods, and you are able to move around the map faster which means less time traveling and more time doing more important things like capping flags and creeping.
Being able to chase down enemy demigods means you get more kills.
Being able to run away means you die less.
Less travel time means more experience and war score.
The most common alternative I keep seeing is Blood of the Fallen. How can anyone believe that an extra 800hp gives them a significant advantage? What is 800 hp if you can't chase down the enemy demigod to finish them off? Sure, you can probably survive the first 1v1 confrontation because you have more hp, and sure, your pretty monks can heal you for 80hp more, but then what? You are still slow, which means you can't do much of anything besides sitting there and taking blows.