Comparing Fedora Core and Gentoo which would you find more suitable of the two for a Web Server?

(Not which is used more, which would work more)

This is not a knock on either distro but you could not have picked to more disparate platforms. Both are equally suitable It really is a matter of comfort. If you plan on exposing this box on the net you really want to be familiar with the os specific methods for securing and updating your box.

here are some pros and cons ..

Gentoo is an extremely flexible distro. You will have the ability to compile every single package on your system for you system with highly optomized compile flags. With the right options across all packages you could really improve performance. The down side is that it literally takes days to do a stage one emerge. Also stage one emerges are very error prone and difficult. I have competed 2 and attempted at least 5 and in the cases where I got a working system I wished I had done a stage 3 and rebuild what I needed. In my opinion the real advantage to using gentoo would be the ease of up keep.. when a new apache comes out just emerge and your done.

As for Fedora there are again pros and cons. Some of the good things are that it will have the host based firewall configured by default and during the install you can simply allow http / https. Another security plus is that FC3 will enable SE-Linux extensions by default which could protect against certain types of exploits that have not even been discovered. On the down side they are not always the fastest in terms up updates and if you use rpm exclusively then expect to wait a few days for the version of say apache to show up. To play the other side if you have SELinux enabled you may be protected , this does not mean you never have to update! but it could buy you the extra day. Also it is a bit of a pain to update an rpm from the FC perspective .. do they patch or bump the rev, then they have to integrate there current patch set possibly adj the build etc..

I personally would use slackware as the base os and use stow to mange the packages in the critical path, in this example apache and any supporting software.

Linux is all about choice and it up to you.