jQuery.ajax is generally better to use if we may require more control of configuration over the our ajax requests now or in the future.  

jQuery.post() only supports a success callback, however jQuery.ajax() supports before Send, success, error and complete callbacks. 

Handling errors is somewhat more convenient and obvious with the ajax calls because they support the success and error callbacks. It would also be more practical to implement logic before sending or when the call is complete regardless of success or fail with the ajax methods.