Edit: Yoav Kutner (Magento CTO) let me know that “in later versions since we optimized the catalog EAV, Magento Compilation is not really needed if you have byte code caching and if it is configured correctly“.
Source: http://www.gxjansen.com/101-ways-to-speed-up-your-magento-e-commerce-website/
Simply enabling Compilation you won't notice much if any difference other than adding complexity with very negligible difference. The sheer amount of 3rd party modules that fail to support this properly means its not worth the time and you're better of in a production environment setting apc_stat=1 using something like this simple module to clear APC's cache: https://github.com/buric/Inchoo_Apc from the admin would be a better alternative than using the compiler.
In short use APC, don't over Complicate things with the Compiler. If you've exhausted all efforts on performance and are unable to add more hardware would be the only time I would even consider it.
apc.stat details
;Setting this to 0 will give you the best performance, as APC will
;not have to check the IO for changes. However, you must clear
;the APC cache to recompile already cached files. If you are still
;developing, updating your site daily in set this to 1
