Whenever I needed to cache some information I relied on timestamps and MySQL, storing the data into a database and fetching it that way. I just read about APC.
APC is so much easier but is it worth converting my previous cache methods to switch to APC besides just less SQL's going through and cleaner code?
To answer literally to the question, yes. Mysql is not a cache, APC is, and thus, is better.
Mysql is an storage option to implement a cache on top of it, but you are implementing the cache with those timestamps you mention and whatever logic you are doing with them. APC is a complete implementation of a cache, both for data and for code.
Performance wise, accessing the local APC cache will always be infinitely faster than accessing a mysql database. Keyword there is local, APC is not distributed (as far as I know), so if you want to share your cache, you'll need an external cache system, such as memcached.