Catch basins and stone basins are two different animals.
By basin I assume you mean grate inlets, where running water is collected off the grade and sent on down the line via drain pipe. They are used to grab high volume, rapidly moving water and get it gone in a hurry.
A stone basin can work in some situations if you have nowhere to run a drain line to, such as sanitary sewer. Collect a bunch of water in one spot and hopefully over time the ground around it will absorb it and take it away. I can see how that would work in some situations, but if you have the option to remove the water completely, that's the best way to go.
French drains are great for what they're intended to do, which is create a curtain to stop water from running in an unintended direction and channel it elsewhere. Sometimes you don't have the option to regrade and a properly installed/designed french drain with fabric, the right pipe and rock will last for quite some time.
Go hard, go fast, or go home