Depends on passive or active barrier.

PASSIVE BARRIER

The team with the highest overall initiative wins the passive barrier. In general, at the beginning of the battle the team with higher overall initiative loads their passives lastand hence win the barrier.

MANUAL BARRIER

The one made by normal gaara and all. This manual barrier forming mystery is considered as a standard attack. If both gaara's are in same position, the gaara with the lower intiative (note: here its individual intiative and not overall) does his barrier forming move second and wins the barrier.