The real physics of water pumping
Water is more or less incompressible. At the pressures at which these pumps work we can consider water to be perfectly incompressible. In which case, how do water pumps generate a pressure differential without any change in volume (this is what it means to be incompressible)? In fact, pumps like the Bathmate use water as a means to transmit forces only. The force is generated by the flexible surround at the base of the tube which you compress to create the partial vacuum. In effect, the flexible (rubber?) base is playing a similar role to air in an air pump. It is the flexible base that is compressible and generates the suction forces. The water simply transmits these forces evenly to your penis. As such, there should be no difference regarding edema/fluid build-up between water and air pumps. All the matters is the pressure difference and duration of pumping. Issues such as ‘mean-free-path’ are an irrelevant side-issue here, that only help to explain the phenomenon of compressibility. Like-for-like, water and air pumps should produce the same effects, except for the small pressure profile caused by variation of water pressure with depth, which for our purposes can largely be neglected. Indeed, if the tube is held horizontally instead of vertically, there will be almost no gravity-induced pressure profile effect at all.
The main advantage of a water pump is the use of (presumably) warm water, which will help to keep tissues moist and warm. However, this, I am quite sure, is largely irrelevant compared with the disadvantages of water pumps, or particularly the Bathmate. The Bathmate has two issues which to my mind make it unsuitable for serious use - is see it more as a novelty item. First, any proper pump should have both a pressure gauge and a quick-release valve. The Bathmate X-series has neither, which to me is a serious problem. When using pumps safely it is really important to know what pressure you are subjecting your unit to. It is also important to be able to release the pressure quickly, if needed. With the Bathmate you have no way of knowing what pressures you are using, and releasing the pressure is awkward and often not very quick. Indeed, if you like to ‘pack’ a pump with your penis, you are essentially trapping the partial vacuum in the tube. This will make pressure release much more difficult without a quick release valve.
In short, there should be no real difference between air and water pumps at like-for-like pressures. Serious users should look for pumps with gauges and quick release valves, which rules out water pumps like the Bathmate.