We are trying to figure out the best way to distribute our applications among our available servers, which are few in number.
Assuming adequate RAM and CPU power, is there any reason we shouldn't run mod_php and mod_rails (Passenger) within the same Apache server? Would they clash or conflict somehow?
There is little risk with running mod_php and mod_rails on the same Apache server.
In fact, Passenger won't affect Apache if it goes down so it is actually a good choice to use with Apache and mod_php. From the Passenger Architectural Overview.
It should be noted that the Ruby on Rails application does not run in the same address space as Apache. This differentiates Passenger from other application-server-inside-web-server software such as mod_php, mod_perl and mod_ruby. If the Rails application crashes or leak memory, it will have no effect on Apache. In fact, stability is one of our highest goals. Passenger is carefully designed and implemented so that Apache shouldn't crash because of Passenger.