The <apex:actionFunction> component also lets you call controller action methods through JavaScript.
In general, <apex:actionFunction> is easier to use and requires less code, while JavaScript remoting offers more flexibility.
Here are some specific differences between the two.
The <apex:actionFunction> tag:
1. lets you specify rerender targets
2. submits the form
3. doesn’t require you to write any JavaScript
JavaScript remoting:
1. lets you pass parameters
2. provides a callback
3. requires you to write some JavaScript
