If we assert that aesthetic experience has no definable cognitive component what makes it an important subject of philosophical interest?

When two people share an experience of something but reach difference aesthetic judgements about the experience, are they experiencing the thing in question differently? Or are they reacting differently to exactly the same experience, and if so, what does that entail? For example, I grew up in Canada and have always liked peanut butter, but I now live in Germany, where few people seem to even know what peanut butter is, and nobody actually likes it. My girlfriend has tried it, but doesn't like it at all. I find it hard to believe that she can eat peanut butter and experience the same delicious taste I am experiencing, and yet not enjoy it. It seems more plausible to me that peanut butter tastes different to her than it does to me, for whatever reason (and obviously, neither of us experience the "correct" taste, just different ones), and that this accounts for her not liking it. Yet on the other hand, the chemicals in the food are the same for both of us, so how can the taste be so different? So...