Both plugins offer real data, but they also record that data differently:
Jetpack Stats, for example, don’t track the following:
- Visits to uploaded documents and files
- Visits from browsers that do not execute javascript or load images
- GoogleBot and other search engine spiders/robots
- Visits by users that are logged in
Google Analytics also ignores the first 2 items on this list, and they ignore some bots, but the list of bots they ignore is different from the one Jetpack uses.
Depending on your site configuration, Google Analytics might track all visits from logged in users, while Jetpack doesn’t do that by default.
This would explain some of the differences between the 2 services. In addition to that, I’d recommend checking your caching plugin settings, if you use one. That plugin may indeed skew the results by caching the tracking code provided by Jetpack Stats or Google Analytics. The best way to figure this out is to turn that plugin off for a little bit, flush your site’s cache, and see if you notice any differences.
I would also be happy to look at your site myself, to make sure both tracking codes work as expected and that no other plugin or widget is actually blocking one of the tracking codes from working properly.
I hope this helps a bit. Let me know if there is anything else I can do to help!