I have Norton Security Suite from comcast if i turn off the firewall can I install Zone Alarm?

I have always felt that Zone Alarm has a better firewall for some reason. After my Zone Alarm Extreme Expired I started using My I.S.P. A.V. == Norton Security Suite 4 and every time I turn around it tells me that an intrusion has been detected. I don't think that Norton is doing a very good job with it's firewall. So ultimately can I disable Norton Firewall and use Zone Alarm without conflicts. I am also thinking about excluding c:\programfiles(x86)\zonealarm from its antivirus scan path. Will this work. What do you think I should do? Thanks in advance my fellow nerds. --GOT ROOT?