Pick up 70-300 IS?

If I already have the 70-200 F4L, how useful would a 70-300 IS be? It doesnt seem as though 300 is that much closer but having IS might be handy. I am really thinking that I would only use it at my kids' soccer and football games.

Thoughts?

I sold my 70-200 F4L and replaced it with the Tamron 70-300VC. The stabilization just makes the lens so much more useful for me. I set it a 5.6, so for me its essentially a 70-300 F5.6 lens. Lose a stop in speed, gain 2 stops with VC.
IMO, If you're shooting your kids outdoors in plenty of light, the FL is going to be more valuable to you than IS.

I have both - 70-200 f/2.8 IS and 70-300 IS (not the L version). I wouldn't get rid of either of them. The 70-300 is great when I have plenty of light, want the extra "reach" and/or don't want to deal with the size/weight/obtrusiven​ess of the 70-200 (the 70-300 is considerably smaller and lighter). I go to the 70-200 when I need the wider aperture, either because of lighting or for the shallower DOF that f/2.8 offers.

100mm extra FL may not seem like much, but it's increasing your existing focal length by 50% - that's considerable if you think about it.