Hydrosol or hydrolate is formed by the water soluble part of Essential oil, mostly polar compounds. These polar compounds are most of the time bioactive compounds. So hydrolate extract are most of the time more active against bacteria.
This is a very common misconception. Actually the essential oil components dissolved in the hydrolates may have antimicrobial effects in pure for, but are not present in sufficient concentrations in the hydrolates to prevent bacterial growth, see:
Labadie C., et al : Hydrosols of orange blossom (Citrus aurantium), and rose flower (Rosa damascena and Rosa centifolia) support the growth of a diverse spoilage microflora Food Research International 76 (2015) 576-586