There is a big difference in these functions. Actually both functions perform the same task which includes the file but the process of including the file a quite different.
This function include the file and make sure that same file will not get included again.
For example if your file say function.php have one function test.
# Output : This code will not generate any error,
# Because include_once will make sure that
# function.php to include only once.
This function also include the file regardless of checking the inclusion of the file in previous code.
# Output : This code will generate error,
# of function test already declared.
If you know what you are doing then its better to use include.
Note: include_once() will check for whole code to check the existance of the file, So its better to use include() over include_once().