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.
Generally, APC will be much, much faster than MySQL, so it's well worth the time to look into it and consider switching from one system to the other. And, as you mention, you will be firing less SQL queries to the database.
More information can be found via Google, I came across the following:
http://www.mysqlperformanceblog.com/2006/08/09/cache-performance-comparison/
If you already have a database running and doing most of your things the first step to improve your performance is to peroperly tune the database. MySQL, properly configured, is very fast. Obviously at some point in time it isn't fast enough anymore and one needs further caches. When caching one thing to consider is that your data might not be consistent anymore. Meaning that you might update data in your primary store (the database) but others stll read an outdated cache entry
Now you've mentoned APC as a possible solution: APC is two related but different things:
An opcode cache works by storing the compiled PHP script in memory. So when requesting a site the PHP interpreter doesn't have to read the file from disk and analyze the code but can directly execute it. This gives a major boost and is always a good thing.
A shared memory cache takes any PHP variable (well, there are a few exceptions ...) and stores it in shared memory in the system, so all PHP processes on the same machine might read it. So if you store the result of a database query inside APC you save time as access to shared memory is very fast compared to querying a database (sending the query to a different machine, parsing it, executing it, sending the result back ...) but as said in the begginning you have to mind that the data might be outdated. And also mind that all data is stored in memory. So depending on the amount of avilable RAM there are limitations in what can be stored. Another big downside of this is that the data is stored in memory only. This means whenerver the system goes down the cache will be empty and everything in there will be lost.