It does sound complicated..
In a nutshell is the 8fun CST HT02 250w motor sold in the Oxy kit able to produce more power and speed than a 'standard' 250w setup? E.G my Halfords Carreras crossfire e-bike..
It's not the motor that decides how much power you get. It's the battery and controller. The bigger the motor, the more power it can take. That's pretty simple, but has nothing to do with how much power it produces.
The same motor can be run at 24v, 36v or 48v. At 48v, it will make double the power it would at 24v, using a controller with the same maximum current.
Next, comes winding speed. Often, the same motors are sold with different speeds. A low-speed one will make significantly more torque at low speed than the equivalent high-speed one and the high-speed one will make more torque in the mid range.
Then there's internal gearing. The faster the rotor spins, the more torque and power the motor can produce. Nearly all geared hub-motors used to have standard 5:1 internal gearing. Now, there's 8:1. 12:1 and more, plus a few in between. Wheel size also changes the speed at which the rotor spins in the same way.
Therefore, we have current, voltage, winding speed, reduction ratio, wheel size and battery that affect how much power (torque) you get at any point in time. This is where all the myths about hub-motors not being able to climb come from. Some combinations can blitz your average Bosch bike in a climbing contest, others would look very sad. Most of the people who say crank-drives are better have never tried hub-motors designed for climbing.
Back to your question: The Oxygen and Oxydrive systems are designed for mid-range grunt, so they can sustain relatively high speed cruising. I haven't ridden your bike, nor tested it's system, so I have no idea of the winding speed, controller current or reduction ratio. if you or anybody else could provide that info, I could convert that into a real-world comparison.