Boost is Sprint without roaming. So if you have good Sprint service in your area, you will get good Boost service.
Cricket runs their own towers. In some areas (like mine), they roam entirely on the Sprint network. However, AT&T just bought Cricket and they're planning on converting them to GSM over the next 12-18 months. So eventually, Cricket will run on the AT&T network and be their branded prepaid division. For right now, they run on a combination of their own network and Sprint.
Actually, AIO is already AT&T's prepaid division. They've made it separate just like Boost is to Sprint. It's likely that they'll use Cricket to boost AIO's coverage even though AIO already uses AT&T's towers (obviously) so the coverage should be close to maxed out.