Not really. It depends on your OS, the version of tomcat you're using,and how many tomcat users you have. RH7.3,8, or 9 work perfectly with tomcat 4.0.3. Not resource intensive at all.
Keep in mind as casey said the size of your server. If you have 512mb of ram and 20 clients using it, yeah you may see issues. We personally prefer using Tomcat on higher end servers 1.5-2 gb of ram.
Also Tomcat is only as good as the people writing the jsp's or servlets. Bad coding equals bad performance. We have two JSP developers at our disposal to go over any coding issues that arise with other clients sites.