Kagome was just a normal girl, until one day she fell into a well that brought her to feudal-era Japan. After encountering hordes of demons and discovering that she's the reincarnation of a priestess, Kagome must now journey to protect a sacred jewel from evil with the help of a half-demon named Inuyasha. Along the way they make many enemies and friends, and travel between the modern and feudal eras.
Amane has a unique power: if she knows someone's true name, she can control his or her spirit. Because of her unusual stoic attitude and suboptimal social skills, she is seen as creepy by her peers and has a hard time making friends. The only "person" she really talks to is actually her guardian in disguise: Hyoue, a dog-demon, who feeds off of humans' life energy. Amane "feeds" him by kissing him in public, which doesn't with help her public image. Amane and Hyoue must keep their powers a secret while fighting the evil spirits they encounter.
Both anime share not only the author, but a similar dynamic and humor. If you liked the humor and character part of the story, you'll enjoy both. Myself, I found Ranma to be very funny, and really enjoyed it. Inuyasha drags a lot, and it is not good as Ranma. But it has it's own merits even if I am not able to appreciate them. If you liked Inuyasha's humor, definitely read Ranma. The inverse is true, although to a lesser extent.