The poetic Eddas say that Freya chose half of the dead in battle and the other half went to Odin in Valhalla, the Valkyries take the slain only after Freya chooses her half. Odin gave this right to Freya as a sign of friendliness for the Vanir, to end the war between them and the aesir and get their friendship. Freya went on to live with the Aesir in Asgard with her brother Freyr, Fólkvangr is in Asgard rather than Vanaheim, Freya's home world.

"Eventually the two tribes of divinities became weary of fighting and decided to call a truce. As was customary among the ancient Norse and other Germanic peoples, the two sides agreed to pay tribute to each other by sending hostages to live among the other tribe. Freya, Freyr, and Njord of the Vanir went to the Aesir, and Hoenir (pronounced roughly “HIGH-neer”) and Mimir went to the Vanir." http://norse-mythology.org/tales/the-aesir-vanir-war/

The 14 stance of the Grímnismál poem of the poetic Edda says:

Folkvang is the ninth, there Freyja directs the sittings in the hall. She half the fallen chooses each day, but Odin th’ other half.

"1866 Benjamin Thorpe in Edda Sæmundar Hinns Frôða “The Lay of Grimnir”" http://www.germanicmythology.com/PoeticEdda/GRM14.html

So according to the historical resources it's Freya who chooses, and Odin gets the other half of the warriors slain in battle.