70-300 EF vs. 70-200 w/extender?

I have a 70-300 IS EF lens and considering moving to a 70-200 F4 L (non-IS) and adding a 1.4x II extender occassionally to get extra range.  I am wondering which will be sharper - the 70-300 or the 70-200 + 1.4x extender.  If it's a wash (or close), I am tempted to go with the L + extender as I will only use the extender maybe 1/3 of the time.  It's for outdoor shots and sports in good light.

Opinions (and of course first hand experience) welcome.