Jepps do get their information from ASA. Where Jepps issue amendments every 2 weeks, ASA only do it (correct me if I'm wrong, it's been 10 years since I used AIP) every 6 months?
However, from memory, don't ASA issue interim (minor) amendments to DAPS to be handwritten on the plate between issues?
It's quite easy to check if your candidate is up-to-date. As Icarus and C&B wrote, there is Master amendment sheet in the front of part A which the owner should have completed on a fortnightly basis.
With each amendment comes the revision sheet which lists all replace/remove and destroy sheets. These should match what is contained in the owners document. All replacement plates issued since amendment 1 will be annotated on one of the revision sheets.
Once a year, Jeppesen issues a master list of every page and its correct date. You check off your document off against this (VERY time consuming). If you have any out of date pages, you advise Jeppesen and can arrange replacement of any out of date pages. Not sure if that come$ at a co$t or not
To put you at ease, many charts that are re-issued by Jeppesen are for reasonably minor changes such as narratives, etc. I think these are such items that would be either amended in the DAPS by hand amendment or NOTAM(?) On Jepps the reason for revision is listed at the bottom of the plate.
Generally Jepps are more up-to-date. But for the price, they ought to be