The finer grit ones are more expensive than oilstones, but waterstones cut faster than oilstones, especially when you move into the fine Arkansas stage of oilstones. When they're both coarse and your oilstone is an India, they'll cut about the same, but the waterstone will wear down faster.
The tradeoff is basically this:
Waterstones are faster cutting and require more maintenance than oilstones. The mess made by waterstones washes away with water. Waterstones are bad for the checking account. Oilstones stay flat nearly forever; with silicon carbide oilstones, it's usually because their abrasives have rounded off and are no longer cutting. Oilstones love all kinds of mineral and petroleum distallates, but your skin, lungs, and workstation might not. The best quality fine grit oilstones can be had at lower price than the cream of the crop waterstone (compare a translucent Arkansas to a 30,000 Shapton Pro or Shapton Glasstone), but good luck finding 'em.