Is water a better nucleophile than bromide?
That is not true. As you noted bromine has a negative charge (and also lower electronegativity than oxygen) and is therefore the better nucleophile (even under these aqueous conditions). Halohydrins are not even usual the result of bromination in water. Special conditions are required to prevent too much $\ce{Br-}$ from attacking the bromonium cation (e.g. certain pH, adding additional reagents as $\ce{AgOH}$ or using $\ce{HOBr}$, see the section Addition Reactions Initiated by Electrophilic Halogen in W. Reusch's online Organic Chemistry book). You would usually expect the dihalide product since $\ce{Br-}$ is already close to the bromonium cation as it forms.