Barrier raises the user's Defense by two stages. Stats can be raised to a maximum of +6 stages each.
>Reflect reduces damage from Physical attacks by 50%, for 5 turns. Its effects apply to all Pokémon on the user's side of the field. If the user is holding Light Clay when Reflect is used, its effects last for 8 turns.
Barrier works like every other setup move. You can the move 3 times in order to increase the Pokemon's defense by x6, so Barrier can give you a higher defense than Reflect. Plus, the Defense boost lasts until the Pokemon faints or is switched out. If you were to switch out your Pokemon that used Barrier, that Pokemon loses its x6 defense boost, and you would have to use Barrier again in order to get your defense high again. Also the Defense boost from Barrier does not get transferred to any Pokemon unless you use Baton Pass. Im most cases, you are better off using Reflect so all your Pokemon can take half of the damage and not have to worry about switching out and using the move again.
Hope this helped!
Source: Pokemon Database pages for Reflect and Barrier.