why different wingtips?
Wing fences were developed way back in 1930s by a German designer to overcome stalling problem of Messerschmitt Bf 109B (not to confuse with wing tip fences). i guess later, post war, when the civil aircraft companies started their production they looked into the matter of reducing the wing tip vortices that caused lot of drag/more fuel cost by having "wing tip fences".
Blended wing tip is a little new concept if you compare to wing tip fences. I think when it comes to reducing induced drag at cruise, so many things apply than just fitting a winglet. Airbus A320, 330, 340 are designed before than 737NG series. I personally think the pre-structural audit decision of fixing winglets (after launching the product) made the Airbus to continue with the fenced tip and Boeing to have the blended tip.
And the latest solution from Boeing is to have "Ranked tips" which does not curve upward or downward but extends the tip chord with a higher sweep angle than of the main wing. you could notice this in Boeing 777-300ER and 787 and 747-8i.
Boeing test their wingtip technologies with a US company which now consult for Airbus as well.
To answer your question, simply having different winglets is a matter of available technology and financially viable decision.
NOTE : Ideas, Opinions, Thought are just to help the question quoted.
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