I've been told a lot of different things on this topic, most of which didn't add up so I did some more research and spoke to people who should know, like an electrical engineer.
If the ESC can handle the current then going to one with a higher current rating won't improve performance because of the higher current. Some people have said that having a higher current rating will mean the ESC pushes more current through a stock motor and helps with jumps...yeah not buying that! From what I can gather the motor draws what it wants, the battery supplies what it can and the ESC just sits in the middle regulating it - so as long as you don't melt/destroy it from the excessive current draw then any should be as good as the next.
However, its more likely that a higher rated ESC will be a higher model for the same manufacturer and likely to be specced with better components which could make a difference. Since you have Hobbywing and they have 3 models its a good brand to look at. The Juststock is 60amp and cheapest, so "probably" has lower quality components which will lead to higher internal resistance etc leading to less of the power getting to the motor. The XR10 stock "should" be better, not because of the higher amp rating, but because of the components, efforts put into R&D and software etc. I don't know if the 160amp XR10 Pro is "better" than the XR10 stock though, as it may be that they are both the top spec model just for different purposes, or it may be that the XR10 pro is the top of the range with the best components and software.
One claim I haven't tested but sounds reasonable (and was from someone who should know, and runs Trackstar, Surpass etc rather than the motor of the week) is that the higher amp ESC will have stronger brakes. I didn't go into why with him as I was talking about motors at the time and it came up when I asked if I should upgrade the ESC. His view is that my old 80amp ESC would perform as well as his 120amp but his would have stronger brakes. Incidentally that ESC packed up and I've replaced it with a SkyRC Toro 120amp, not for the higher amps but its a good bang for buck ESC and it wasn't a planned upgrade, rather a forced one so the money mattered.
So if the Justock is working for you then stick with it. If its playing up and you can get a good deal on a combo since you're buying a new motor already, then do that. Or if you just like upgrading and want something shiny and new, do that.