another 5D3/1DS3/6D related thread
I was in the same predicament few months back and you have to think about this.
The 3 are great cameras and everyone of them has its disadvantages.
the 1Ds3 doesnt do video , do you use video ever? as well the preview screen is not great.
the 6D if focusing is the issue for you this will be worse as it has less focus points and you dont have 1/8000 for that bright days at minimun aperture.
the 5dIII will be the best of the 3 if you dont my the stigma of its predecessor. the 5dmkii was a great camera with some problems but still a great camera and the 5diii its even better with most of the problems fixed.
with the problem you have with the focus it looks that either you have it in the wrong setting or you might be at fault here. for fast scenes ( if you mean a quick snap somethign jsut came up or something interesting apear) you may need to expand to cross or the next square not sure if the 600D has that options. if by fast scenes you mean sports or peaople running etc you have to make sure you have AI Servo (remember to hold the focus button).
As well i have found that a lot of people havent change their cameras to a 2 button set up one for the focus and the other one for the shutter. if you havent done this please do and this might fix all your issues of focus.
hope this helps
I own the 5Diii (main) , 6D (assistant) and 7D (fast sports) all have different purposes.
I'll shoot you anytime; lol