Client and Server mode are JVM startup options. Basically, they're 2 different optimization strategies, with Client mode being geared towards fast application startup and Server mode being geared towards long-term performance.
Actually, last time I looked, I think that Tomcat was starting up by default in Client mode, which is simply the default Sun/Oracle JVM startup mode. But you should be able add an entry to bin/setenv.sh (or .bat) and override that.
The difference between the modes isn't usually going to kill you if you start under the "wrong" mode. Presumably the JVM is going to adapt as it sees how it's being used.
An IDE is no substitute for an Intelligent Developer.
Actually, the difference is huge. The server VM is about twice as fast as the client VM in my experience. In fact, newer JVMs are shipped without the client VM completely. You can find more about this on http://java-monitor.com/forum/showthread.php?t=552, scroll down to the executive summary if you don't want that whole reading thing.
Tomcat by default leaves the JVM to decide for itself. On machines with limited RAM and only one CPU it will default to the client VM.