Time in Shikoku vs Kyushu

Hello! My friends and I are booking a trip to Japan for 3 weeks in late September. Right now our itinerary is pretty open, but we're starting to narrow certain places down that we wish to visit. I've been to Japan 4 times now and have seen lots, so we're really looking for the scenic, traditional Japan experience. A section of our trip, about a week and a half, is a toss up between us going to Shikoku, then make our way to Yakushima, or explore Kyushu before Yakushima (Yakushima being the one constant).

My question is, between exploring Shikoku and Kyushu, which is the better experience? We're planning on renting a car in either area to get around.

Thanks for any help, we're a little lost right now, and I'm looking to craft a great itinerary for all of us that includes ample natural scenery and traditional man-made sights.

Kyushu has more to offer than Kyushu in many respects, especially mountains and onsen. Both islands have interesting cities and castles. Shikoku is generally a little bit more off-the-beaten path, but Kyushu, too, has many remote areas. It really comes down to your personal interests.

Kyushu attractions:
https://www.japan-guide.com/list/e1108.html

Shikoku attractions:
https://www.japan-guide.com/list/e1107.html

In my experience I equally like both Shikoku and Kyushu. Shikoku is less known so its fun to go to a less popular place, but Kyushu has alot of great places. There is a ferry that connects Shikoku and Kyushu off of Sada cape in Shikoku to Oita city in Kyushu. My favorite places in Kyushu are Miyazaki prefecture and Kagoshima prefecture, going down to the most southern point of Kyushu and main islands of Japan Sata cape (which has a similar name to Sada cape in Shikoku). Miyazaki has alot of palm trees so it gives off a nice tropical atmosphere. Sata cape and Sakurajima island in the bay of Kagoshima are really lovely. The pottery area of Nagasaki is neat too (Arita and Imari). In Shikoku the karst, and the coastline of Kochi prefecture are very lovely along with the Iya Valley of Tokushima. Both Kyushu and Shikoku have very delicious local specialities, both food islands. But since Kyushu is a bigger island of the two maybe that would make more sense to pick more time for Kyushu since they have more stuff.

3 weeks? You have ample time to visit both.

Kyushu is about 3 times bigger in size and sights.

With 3 weeks, assuming you fly into Tokyo, why not take an internal flight to Shikoku, travel there, take the ferry to Beppu and then do some of Kyushu, heading down to Kagoshima for the fast boat to Yakushima, and then home?
Or Shikoku, then ferry from either Takamatsu via Naoshima to Okayama then to Kyushu or ferry from Matsuyama to Hiroshima and then train to Kyushu?
Plenty of great options...

Thanks so much guys for the help, I think maybe we're going to try to squeeze em both in. Again, thanks for the help, I can always count on this forum for itinerary tips!