How can I color/style match concrete patch to old sidewalk? See image
Your repair will never match... perfectly. 

Your first question: How to remove the bad repair? It will be difficult and you won’t be able to remove it all. I’d start with a chisel and try a grinder when it is low enough that the marks can be covered during the repair.   

I’d consider cutting that entire section out and replacing it with a new pour...especially if the walk is in an important location, like a front walk. 

Second question: How to repair? I’ve seen concrete repair by “old-timers” who take great pride in matching color and texture. However, they don’t match it perfectly. 

If you want to try, I’d: 1) find a place to experiment so you can pour 8-9 small samples until you get it acceptable, (you’ll need to wait until it dries...28 days between samples,) 2) use concrete coloring and mix it into your mix, 3) find a sufficient amount of rocks that match in size, color, etc.

You will need to hand place the rocks to the same spacing, depth, etc. as the existing. 

It’s more “art” than production. It takes a lot of time and patience.