As has been covered many times on this forum, using an opcode cache can make a dramatic difference to Moodle CPU performance, i've seen up to 50% improvement on some servers.
In the Moodle 1.x days a lot of people were using eaccelerator, as this was one of the best options at the time. Over time the 'official' php alternative, APC has become a lot more robust and widespread.
We've recently discovered some bugs (MDL-39432, MDL-36060) when Moodle is used with eaccelerator. Upon investigation, there are some major php features which eaccerlator does not support. More concerning than that is that there seems to be no activity from the eaccelerator project to fix the problems and these are bugs which will reach far wider than just moodle.
So this post is just a heads up, to advise you that I would recommend not using eaccelerator if you have the option on a new install or future change. The lack of support and or changes from them indicates the project is not one i'd like to trust my production Moodle install on.
We are looking at whether we should explicitly drop support for eaccelerator in Moodle in the future. You can follow along with that discussion in MDL-39430