I want to get some input as to which has a better success rate:
Brown cutting or Green cuttings?
What thickness also has a better success rate?

Thanks.

I would say green because the growth is young. Just don't let it dry out. I'm testing a grow cup on one of my brown cutting while the greener ones are in a greenhouse type thing. 

From my experience hardened off brown wood roots better for me.

I have success to root both green and brown branches. However, the leaves on green branch will rot or fall off. Not big deal, will grow back eventually. 

IMO, hard wood with green buds.

The key thing is how fresh the cutting is. If you get fresh growth and store it in the fridge for awhile then it's chances of rooting start to diminish. I found that the faster you get the cutting into your choice of rooting medium like moss or cubes the better the results. I've had fresh green growth cut from a tree and it rooted in a week and the same results for some dormant wood that was cut from the tree, straight into some rooting cubes. IMO for either one the fresher the better.

Does the thickness of the cuttings play a role in its success?

As for thickness playing a role in success, I would say yes. A thicker cuttings would have a larger reserve of food to help it start to grow. I have had very skinny cuttings root but nowhere near the success rate as a thicker cutting. I think a good size is about as fat as a ''sharpie'' marker, maybe 1/2 inch thick or even slightly thicker.

rooting is not the problem when it comes to which one will do better. my biggest problem is keeping green cuttings alive after they have rooted.