I really like both of these prefectures. In addition to some of the sites others have mentioned in Yamaguchi, Hofu Tenmangu Shrine and Motosumi Inari Shrine. Yamaguchi City has some nice temples, too.
Not much has been said about Saga, but Saga is a great and highly underrated prefecture.
The sites listed by Japan-guide (this website) are good.
-Yutoku Inari Shrine is highly worthwhile. It's definitely among the most beautiful in Japan. Hizenhama Historic district is well-preserved, as well.
-Yoshinogari is a great historic site. It took a lot longer to explore than I expected.
-Arita's historic district is pretty.
-Okawachiyama is also a picturesque pottery town.
-Ureshino Onsen is a great onsen that has a noticeably great feeling on your skin. The only other onsen I know of like it is Ikeda Onsen in Gifu, so it's definitely unique.
Places not found on this site:
-In addition to Karatsu Castle, Nagoya Castle, etc. listed on this site (Japan-guide), the Former Takatori Residence in Karatsu is also worthwhile.
-The Takeo Onsen link here just talks about the onsen and the library, but it leaves out Mifuneyama Rakuen Garden and Keishuen Garden, both of which are worthwhile.
-Ouo Shrine has very famouss torii gates leading out in the water. It is popular for pictures, and the experience differs depending on the tide.
-Arita's Porcelain Park is very beautiful.
-In Saga City, Saga Castle is interesting and Furuyu Onsen is not well-known by foreigners. Kyoseki Park looks interesting, but I've not been there.
You can see more about Saga here:
https://en.wikivoyage.org/wiki/Saga_(prefecture)
Saga and Yamaguchi both have a lot of interesting sites, so there is no wrong choice.