What is the difference between bridge and routing firewall ?
How they both works and what are the security advantages/disadvantages for both scenario ?
A routing firewall participates in the IP process, whereas a bridging, or transparent, firewall does not. A transparent firewall acts more as a tap on a line, while a routing firewall has to forward traffic onto its next destination.
The advantages of a transparent firewall are that it can be installed in-line between two devices without having to reconfigure the IP subnet used as the interfaces on the firewall are unnumbered. From a security perspective a transparent firewall is quieter, as it does not participate in IP connections an attacker may not even know it is there unless something is blocked. An attacker will have difficulty determining the type of firewall being used.
The advantages of a routing firewall is that as it participates in the IP protocol it can do network address translation, port translation, and tricks like source port scrambling to make fingerprinting more difficult. A transparent firewall provide these types of services.
As for which to use it depends on the problem you are trying to solve. Routed firewalls provide the most capability and flexibility, but transparent firewalls can be inserted into connections without requiring substantial network changes.