Neither. The reactivity of any given substance is a characteristic of the substance; it doesn't matter what the substance is in.
Most metals are reactive with acid, because metals tend to lose their valence electrons easily, and acids are electron receptors. Some non-metallic compounds are also reactive to acid, again because they are able to give up electrons to the H+ in the acid.
There are some substances which are reactive to water, most notably elements in the Alkali Metal family including sodium, lithium, and calcium. These elements are also reactive to acid.
In many cases reactions need a medium to occur in. Many ionic solids will be non-reactive in the dry form but will react if they are first dissolved in water. This is because water causes the substances to separate into their component ions, which can then react with other ions. Dissolving the substances in acid would work also, but this is because all acids contain water. In either case the liquid is just a medium for the reaction to occur in. The reactivity of the substances is due to their chemical nature, not to the medium they are dissolved in.