I agree. I have both Fuji and Canon lenses. The Fujinon are just a bit softer than the Canon. With your greenscreen work the sharper image might be better for you. The Fujinon also have tendency to look even softer when the extender is flipped in. Speaking of which, the Canon 4.7 is a great lens, but if you are having to do longer zoom shots with the extender on, you will definitely notice the difference in the clarity through the extender. You may want to consider at least having one lens that is longer for the times you need to shoot with a compressed perspective or drop the depth of field. I don't think you will necessarily need the longer lens for your green screen work, but it might be helpful working with other set ups.
Just my thoughts,
Tracy Eakes