suPHP and FastCGI are the PHP handler which interpret the PHP code in your web application and process it to be sent as HTML (or another static format) by your web server. Web servers can not handle the PHP themselves that is why they need the program to run the PHP. On Apache, there are mainly 4 types of PHP handler as below -
It runs the PHP outside of the Apache. It will run the script as user instead of Apache that is if you have your own CMS then you can upload the PHP values from your web application. Benefit of this is, if there any attack of particular user that will be restricted to that particular user as the suPHP is user based.
But it is slow and takes more resources on the server. It can not handle the high usage operations so it's not recommended.
It is recommended PHP handler. It is very secure. It has feature of OPCode caching and memcached. It will use the more memory on the server but very fast so you can have the FastCGI.