If you really want to do a lot of shooting of little league or other sports, get a version I of the 100-400L and you will be covered from wherever you sit at the field. Little league fields' outfield fences are 200 ft from home plate and if you want to shoot the batters from the bleachers anything less than 300mm just won't cut it from there, especially on a full frame. It's great with lots of light, but if it gets cloudy, your 6D's low light/high ISO capabilities can handle it no problem.
Ill check into that one.. i assume its like f3.5-5.6 or similar, not a constant 2.8.. maybe not great for night games... i dont like the 100 end of the spectrum on that so much, feels too tight in spec anyway.
How about the new Tamron 18-400.. i've watched a few reviews for it and it sounds tantalizing and not super expensive though again not a 2.8