We get asked this a lot, and the honest answer is there's no single right choice. Both are excellent, and a lot comes down to your stylist and your priorities.
Genius Wefts are actually the more widely used of the two, even though they're the trickier method to apply. Most extension specialists are trained in the technique, so it's often the one your stylist already knows best, and it does need an expert hand rather than a DIY job.
Butterfly Wefts are the easier of the two to fit, simple enough that some people manage them at home. They're brilliant for most people, flat, comfortable, and reusable.
Where Genius Wefts pull ahead is invisibility. If you have thicker natural hair and you're chasing length that genuinely disappears into it, Genius Wefts are usually the better call. Their finer, flatter build means they stay hidden even under hair that would otherwise make a weft harder to conceal.
Thin or fine hair works beautifully with either method. From there, it's really a question of what your stylist is most confident applying and what finish you're after.