According to the specs, the Mini Master 160 has an ISO-100 GN of 43, vs the 560's GN of 39. So the Mini Master is very slightly brighter.
The Mini Master is AC only vs the YN560 being battery only (without hacks).
The Mini Master has a modeling light but none on the YN560.
The Mini Master can be adjusted from 1/1 to 1/8 power, the YN560 from 1/1 to 1/128 power.
Neither unit has a built-in mount for modifiers such as beauty dishes, softboxes, etc. However, the Mini Master has a built-in umbrella clamp, while the YN560 can utilize an L- or S-bracket to mount modifiers.
I might be inclined to buy some mini-master's for background lights or hair/rim lights; I could probably make a snoot that slips over the head and gets retained by a thick rubber band or velcro. The inability to a softbox or beauty dish, or overpower bright sunlight, would make them less desirable to me for main lighting.
I wouldn't buy a 560 Mk II at all. I do own and might buy more YN560 Mk IV's to pair with my YN560-TX, allowing me to adjust the flash settings from the camera. I would use these with Godox S-Type brackets to mount umbrellas and Bowens-compatible modifers.