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As per the definition in WikiPedia (http://en.wikipedia.org/wiki/Bugtracker), A bug tracking system is a software application that is designed to help quality assurance and programmers keep track of reported software bugs in their work. It may be regarded as a sort of issue tracking system.

The two most popular open source bug tracking systems are Mantisbt and Bugzilla

In this writeup we are going to enlist some advantages and disadvantages of using either of the tools for issue and bug tracking.

Bugzilla
Its a Bug tracking system. Inherently web-based, written in Perl, and uses MySQL as its database back-end.
Advantages

1. Captures lots of data
2. Powerful reporting

Disadvantages

1. Slower compared to Mantisbt
2. Complicated to setup
3. Can get overwhelming too soon
4. Greater learning curve

Mantisbt
Mantis is a popular free web-based bug tracking system. It is written in the PHP scripting language and works with MySQL, MS SQL, and PostgreSQL databases
Advantages

1. Easy to setup, customize and maintain
2. Easy to understand
3. Can be easily adapted to an organizations software development process

Disadvantages

1. Compared to Bugzilla reporting is less sophisticated

Having worked with both, I will recommend Mantis simply because its is easy to use, adapt and maintain. Bugzilla is huge and has a lot of mumbo-jumbo that you may not need. Another advantage with Mantisbt is that it is cleanly coded and is hence easier to tweak and customize. But, you may find reporting a little weak in mantisbt.

Bugzilla is better suited for technical users, while non-tech users feel more comfortable with Mantis.

So, to conclude if you need a powerful issue tracking solution that is easier to setup, customize, use and maintain and if you feel the existing reporting in mantisbt satisfies your need then GO for Mantisbt.

Else, you can evaluate Bugzilla and other web based bug tracking systems. Bugzilla may get really overwhelming if you do not have a very complex need.