T5i vsT6i vs 60d af points

I'll start the ball rolling.  Firstly you don't say what camera you already have and it is misleading to list the cameras you'd like to have in your profile.

I have the T5i/700D and I am a generalist shooter which may or may not include black dogs though does include wildlife including birds.

Which camera you get of those cited is less important than your technique but there are a few pointers:

1) I tend to use Centre Point mainly and where necessary focus on the eyes.  All points is ok except it tends to lock onto the nearest point.  All points is however useful if I am tracking a moving object (bird, plane etc) and I can't keep the Centre Point on it readily.

2) If the dog is moving you will still have issues if the dog is not moving in a consistent fashion.  AI-Servo can only be so much intelligent and needs a second or so of consistent movement to predict where the subject will be.  That's how it works.

3) You need to be careful of focussing on a black dog (or any uniform object).  Some contrast is usually needed though you will have it if focussing on the eyes.

4) You need to be careful with metering and you may be better to go for manual metering otherwise you may end up with black dogs looking grey and everything else looking too bright.

Hope that helps with your deliberations though it would help others if they saw samples of what you are doing or would like to achieve especially whether indoor (lighting) or outdoor (motion).