Yes, comparing public and external keywords, the external keyword will consume lesser gas than public keyword.
The difference is because, in public functions, Solidity immediately copies array arguments to memory, while external functions can read directly from call data. Memory allocation is expensive, whereas reading from call data is cheap.
The reason that public functions need to write all of the arguments to memory is that public functions may be called internally, which is actually an entirely different process than external calls. Internal calls are executed via jumps in the code, and array arguments are passed internally by pointers to memory. Thus, when the compiler generates the code for an internal function, that function expects its arguments to be located in memory.
For external functions, the compiler doesn't need to allow internal calls, and so it allows arguments to be read directly from call data, saving the copying step.
As for best practices, you should use external if you expect that the function will only ever be called externally, and use public if you need to call the function internally. It almost never makes sense to use the this.f() pattern, as this requires a real CALL to be executed, which is expensive. Also, passing arrays via this method would be far more expensive than passing them internally.
You will essentially see performance benefits with external any time you are only calling a function externally, and be passing in large arrays.