lenses:70-300 IS 4-5.6,
I take it this is the non-L?
If it is the L then definitely use this lens for outdoor soccer.
I suspect the center point of the 6D focuses better for soccer than the Rebel, although they did remove the helper points for the center that that 5D2 had which seemed to be extremely important for field soccer shooting with that particular body so I really don't know though.
70-200 is very short for field soccer, although it makes a nice lens on a backup body for the occasional close shots.
On 20MPish FF 300 2.8+1.4x TC was nice = 420mm.
Try both in both combos and see how things go.
300 f/4 non-IS can be found used for maybe $650 (this one is probably better to use without TC for sports although it is fine to use the TC for birds sitting around) although perhaps the 70-200 2.8 IS II + 1.4x TC these days would do almost as well???
I suspect the Tamron 70-300 VC would work even better than the 70-300 IS non-L, although I never tried the tamron for sports. The 70-300L focuses 50% faster than the tamron and has more precise AF.