EEPROMs are under-rated in my view. It takes some time to learn, but is nice to be in control of the data flow. And EEPROMs are very very cheap.
By contrast I found SDs as really mysterious pieces of a devilish character. Not to mention that SD are really hard to find. Perhaps there is SDHC or even better SDXC readers for Arduino, but I could not find one.
On the other hand, more complex tasks or high volume of date looks to me as a tasks for Raspberry Pi or similar, rather than one for Arduino.
But is a matter of taste, of course.