Aside from audio what does the m8 really have over the shield tab in terms of gaming? Nothing lol, gaming is all about the cpu/gpu, which the shield gets the +1, it doesn't have as much ram-- but you'll never use it all for anything out this year or the next
Firstly, the M8's Snapdragon processor performs better on higher resolution games than the shield's Tegra 4. You can find benchmarks that support this. However, for gaming on Android (for the most part) the Tegra will have a slight advantage since most games aren't heavy or demanding. It's important to note that this is a very small gap in performance though and the average user wouldn't tell the difference. If you wanted to get REALLY technical, there are a couple more features the M8 has, but that's irrelevant.
In addition, any smartphone can do what a shield can't - be used as a phone. While there are apps that would allow texting and calling over WiFi, a phone is a phone. I believe the OP was looking to purchase a new phone, and right now the One M8 is pretty hard to beat as far as Android phones go.
Anyways, case in point I never said the M8 was a more viable option than the shield. I simply think that a smartphone is a better investment than a gaming tablet/controller.
Lastly, to answer OP's question, the Samsung S5 mini will be capable of running CH, but depending on what you're paying for it, there may be better alternatives.