Short answer: it depends on the teacher. Find a good teacher and if both are good pick the one you like best.
Longer answer: both can be good for self-defense, depending on whether the teacher is actually interested in teaching you that. I've also seen sports-focused dojos in both styles which can develop useful skills (coordination, footwork, quickness) but may not give you the stopping power that makes karate so interesting, in my opinion. As far as stylistic differences go, shotokan is an older style with deep stances and (traditionally) a focus on powerful strikes while wado ryu has a higher, more mobile stance and integrates evasive body movement as well as throws from Japanese jujutsu.
