Your routers firewall is likely to be very similar to the windows XP one, in that it monitors inbound traffic only (unless it specifically says otherwise), but not outbound traffic.
So in comparison to ZA the router firewall is only doing half of the job and the free version of ZA is crippled in the level of outbound protection it gives in the hope you will buy the Pro version.
Zone Alarm free works fine with avast and has a reasonably friendly user interface, however, the free version is becoming bloated with trial ware and is also crippled as far as outbound protection goes In the Program Control, configuration area, the slider will only goes as far as Medium protection, if you want more you have to buy the Pro version.