What is the best firmware for my Sony PSP

PlayStation Portable system software

 is the official, updatable firmware for the PlayStation Portable. Updates add new functionality as well as security patches to prevent homebrew applications being run on the system. Updates can be obtained in four ways:

• Direct download to the PSP over Wi-Fi. This can be performed by choosing [Settings], [System Update] from the XMB.
• Download to a PC, then transfer to the PSP via a USB cable or Memory Stick.
• Included on the UMD of some games. These games may not run with earlier firmware than the version on their UMD.
• Download from a PS3 to a PSP system via USB cable. (Japanese version only)

While system software updates can be used with consoles from any region, Sony recommends only downloading system software updates released for the region corresponding to the system's place of purchase. System software updates have added various features including a web browser, Adobe flash player 6 support, additional codecs for images, audio, and video, PlayStation 3 connectivity, as well as patches against several security exploits, vulnerabilities, and execution of homebrew programs.^[1]The battery must be at least 75% charged or else the system will prevent the update code from installing. If the power supply is lost while writing to the system software, the console will no longer be able to operate unless the system is booted in service mode or sent to Sony for repair if still under warranty.

The latest reported firmware version shipping pre-installed on new PSPs is 6.20^[2], which was released (as of June 29, 2010). The latest version of the system software is 6.31 (as of July 29, 2010).

Custom firmware (CFW)

Custom firmware is an alternative to official firmware. Custom firmware is a slightly modified version of a specific official firmware. The most notable modification is the ability to run unsigned code, known to many as "homebrew".^[39] Other modifications follow.

• The ability to load UMD games and videos, saved as ISO images (or compressed as CSO files) from the memory stick
• A recovery menu, for executing extra modules elsewhere on the file system^[40]
• Access to internal flash drives where firmware and registry are stored

What is the best firmware for my Sony PSP

If you are using original Sony PSP version it is better to have the latest firm ware. 

BUT if you have to choose between CFW 5.00 M33-6 or 5.50 Gen D3 , I will advice to installed 5.00-M33-6 from Dark Alex.

Why Dark Alex?

Dark_AleX .... in wikipedia :

Two PSP-1002s running on 5.50 GEN-B.

Dark AleX (aka Dark_AleX, Dax) is a Spanish programmer who writes homebrew applications for the PlayStation Portable. Dark AleX, as well as other variations of the name, is a pseudonym under which he works. ^[6] One of the drawbacks of downgrading the PSP is that new official media may require the presence of a new firmware edition. Dark_Alex had released a custom firmware called "Dark Alex's Open Edition firmware" or "Custom Firmware (CFW)" which opens the firmware but allows users to use the existing feature set of the current edition. Sony quickly patched the firmware again, continuing the cat-and-mouse game with the hackers and users.^[7] In 2006 Sony released six updates to the system firmware and in 2007 they released another six updates.^[3] In July 2007 Dark_AleX officially stopped his work on the PSP, citing perceived problems with Sony as one of the reasons for his departure.^[8] Some people even suggested that Dark_AleX was paid by Sony not to release any more custom firmware, but Sony denied this.^[9]

Custom Firmware allows the running of unsigned code such as homebrew applications and UMD backups, emulators for other consoles, as well as PlayStation games when the disc images are converted into PSP format.^[10]

There you go man .... The PSP CFW king! DARK ALEX