The essential difference (from a water-heating standpoint) is that a wood fired hot tub heater cannot keep your hot tub's water at an exact temperature, as the other heating options can. Moreover, the heat will tend to stratify, meaning the hotter water will rise to the top, while the cooler water will sink to the bottom. To combat this, use a paddle or similar implement to stir the water occasionally while you soak. The optional Filer option will help reduce the stratification by force mixing the water.
Controlling the temperature and heating times will depend on the type of wood, the water temperature, and external outdoor temperature. However by using the same type of wood a user will quickly get the feel for the right amount of wood quantity and the heating time required to reach the optimal water temperature. It is important to mix the water to get an accurate water temperature before you enjoy your hot tub as the top may be hot but the bottom is only luke warm.
The heat up time of a wood fired hot tub will depend on the water volume and the size of wood fired hot tub stove that is used. This chart below is an approximation based on a Timberline Wood Water Stove. For most hot tubs a Medium "Blaze" size stove is recommended (55,000 BTU) for our smaller Ofuro Japanese Hot Tubs a smaller "Camp Fire" Model (30,000 BTU) is recommended,