The browser cannot determine anything when it comes to the canvas element and the rendering as it is a passive element - everything in it is user rendered by the means of JavaScript. The only thing the browser does is to pipe what's on the canvas to the display (and more annoyingly clear it from time to time when its bitmap needs to be re-allocated).
There is unfortunately no golden rule/answer to what is the best optimization as this will vary from case to case - there are many techniques that could be mentioned but they are merely tools you can use but you will still have to figure out what would be the right tool or the right combination of tools for your specific case. Perhaps layered is good in one case and perhaps it doesn't bring anything to another case.
Optimization in general is very much an in-depth analysis and break-down of patterns specific to the scenario, that are then isolated and optimized. The process if often experiment, benchmark, re-adjust, experiment, benchmark, re-adjust, experiment, benchmark, re-adjust... of course experience reduce this process to a minimum but even with experience the specifics comes in a variety of combinations that still require some fine-tuning from case to case (given they are not identical).
Even if you find a good recipe for your current project it is not given that it will work optimal with your next project. This is one reason no one can give an exact answer to this question.
However, when it comes canvas what you want to achieve is a minimum of clear operations and minimum areas to redraw (drawImage or shapes). The point with layers is to groups elements together to enable this goal.