The second line, “I’ve never tasted caviar,” is more straightforward in terms of referring to a life event when read without any other context. “I haven’t had caviar in a long time” might refer to a specific occasion or evening. So, you’re at a party and you’re looking at the many foods on offer and you think to yourself, “I haven’t had caviar.” This indicates you haven’t had caviar at this event or on this specific occasion.
However, as always, context is crucial. Whether someone asks you if you’ve had a lot of experiences in life or if you’ve tried a lot of various meals, you may respond, “I haven’t had caviar,” and it’ll be clear from what you’ve said so far that you’re referring to your whole life.
“I’ve never tasted caviar,” you’d say while talking about life events.
“I’ve never eaten caviar” would never be utilized in a live situation unless you’re eating it for the first time and adding the word before.
Comparing past and present periods is one of the reasons for present perfect, but prepositions and adverbials, like as “never,” are also important.