Oil seems to help prevent the stone clogging, while it's in use. If you don't take soap and a brush to the stones, on occasion, they fill with metal particles and oil, and get glassy over time. That slows cutting pretty significantly, but it takes years of sharpening to really be an issue. These stones take a fair bit of abuse.
Arkansas stones tend to be a fair bit less expensive than decent diamond stones. Nothing wrong with diamond stones: they do the same job, and probably more quickly. They're just expensive, and they don't last as long. My dad used to wear out diamond stones in a couple years, sharpening chisels. Arkansas stones will last generations (I've got my granddad's old pocket stone). They're not fast, or fancy, but they're cheap, long-lasting, low maintenance, and they do the job.
What kind of flat rock (synthetic, water, Arkansas, diamond) you like really is just a matter of preference.