The BBS02 250 and 350 W are identical. The controller is set at the factory to different A values. The 350 W also exists in a 48 V version which is a de-tuned 500 W version IIRC. The 500 W motor weighs about 500 g more so most likely contains more copper winding.
Now if you want to be confused... The BBS02 controller can be programmed to 18, 20 or 25 A which means you can have 250, 350 and 500 W versions of the same motor. Until recently there was one on the market, a 250 W stamped de-tuned BBS02 500 W motor.
Other than extra copper wire in the heavier 500 W motor they are identical and cost the same to manufacture. Price difference between a 250 W and 350 W motor are purely marketing differences - if it is more powerful it should cost more...
A BBS02 250 W reprogrammed to 25 Amps will be more prone to overheating if abused than the 500 W version at 25 A.