suPHP is mainly about security. It will execute PHP scripts with the owner’s account. So, if you want maximum security, use suPHP. But, the biggest problem is, you can’t use any opcode caching modules! No caching, so, if you are willing to boost the speed of your site with a caching modules like APC, don’t use suPHP.
DSO is one of the fastest php handlers. You’ll also be able to use opcode caching with DSO. So, it’ll be great for people who need speed! But, when it comes to security, DSO is a very bad idea. DSO runs the scripts as nobody. Not only for security, also when it comes to WordPress Hosting, DSO might be a very bad idea. Most of the times, it will cause WordPress to throw permission errors and break your system. The biggest problem is, you won’t be able to install plugins and update the system easily.
FastCGI is one of the most commonly used handlers. If used with suEXEC, you don’t have to worry about the security because it will run the script with the account of its owner. It also supports opcode caching. So, it looks like FCGI is good for both security and speed. But, it also have a problem. Memory usage! FastCGI will run each application as a separate process consuming a lot of memory. So, you might have to think twice before using FCGI.