I have less experience making wines than beer. Brewcat and others have more experience. I looked at the reviews, instructions etc on the NB wife you purchased and a review of apothic dark wine A Review of Apothic Dark Wine: Is This a Good Bottle? - Vino Del Vida
In the NB reviews they mentioned that the kit did not have a high enough level of tannins and the review of apothic mentioned it medium in tannins. I suspect that the lower level of tannins in the NB kit may be what your wife does not like. An educated guess (not the wine:))
Wine tasting is sooooo subjective. Open a bottle of apothic and your wine and do as Brewcat suggested letting it breathe etc. Do a blind taste test. Pour three glasses, two of one type and one of the other. Ask her which of the two glasses taste the same. If she can’t tell the difference then end of problem all three taste the same. If she can tell the difference, ask what she likes and dislikes between the two. If it is tannins she may notice that one wine has more of a puckering feel in your mouth. A high tannin level gives a mouth puckering feel sort of like a tea steeped too long with no sugar or milk feeling. The wine wont have that much pucker to it but it may have some. Ask about sweetness etc. This should help you and us pick out the next kit to try.
I once did a taste test of an aged Australian cab bottle aged vs stainless steel aged. Used three glasses as described above. One person loved the first glass out of bottle and absolutely hated the second glass! Only one person was able to identify difference between bottle aged and stainless steel aged but could not decide which one was better. That’s how taste test go with untrained tasters.