Which destination would you recommend for 3 days: Miyako-jima or Kagoshima & Yakushima Island?

I’m travelling through Japan with my brother this summer, then ending our trip in South Korea for the last 5 days, flying home from Seoul. We have most of our trip planned, spending a week in Tokyo (with one or two day trips to surrounding areas possibly included), one day/night at Lake Kawaguchi, and another week split between Kyoto and Osaka.

We have three days still left to plan between Osaka and Seoul, and we are trying to decide between two options: either taking the bullet train from Osaka down through Kyushu, and spending a day in Kagoshima and two days in Yakushima Island, or flying straight from Osaka to spend three days in Miyako-jima in Okinawa Prefecture.

I know that both destinations are extremely beautiful, each in their own way. Going to Miyakojima would allow us to explore the unparalleled beauty of its beaches, do some snorkelling, really slow down and relax, and experience Okinawan culture, but going to Yakushima would allow us to hike through its lush, ancient forest (and we could visit Isso beach).

I am hoping to get your opinions on which destination would be more worth our time. What are the pros and cons of each, what are some important considerations we should take into account, what were your experiences if you visited either one, and ultimately, which one would you recommend if you had to choose? Thank you in advance for your help, it’s greatly appreciated!