A grown diamond is a diamond. Same carbon, same lattice, same fire, graded by the same laboratories. A jeweler cannot tell them apart by looking, and neither can anyone at the party. What separates them is origin, price, and what the two of you decide those mean.
The arithmetic
Lab-grown prices have been falling for years and now sit at a small fraction of their mined equivalents. In practice, the same budget buys a dramatically larger or finer stone. For buyers whose goal is the most beautiful object their money can produce, the argument tends to end there.
The honest caveats
Neither stone is an investment. Mined diamonds resell badly; grown ones resell worse. Production costs for grown stones keep drifting down, so the identical stone may well cost less in a few years, a thought that bothers some buyers and leaves others entirely unmoved. And some people simply care that their stone spent a billion years underground first. That is not a position arithmetic can argue with, and it is not supposed to be.
It is one person's opinion that settles this question, and it is not yours, and it is certainly not ours.
How it actually gets decided
Couples who prize size and budget go grown and do not look back. Couples who prize tradition and heirloom weight go mined and consider the premium part of the point. If you do not know which couple you are, the discreet inquiry through her sister is a time-honored instrument.
The short of it: both are real. Grown wins the arithmetic, mined keeps the mythology, and her opinion outranks every paragraph above.