By West Africa, I mean countries like Nigeria and Ghana, and by East Africa I mean countries like Kenya and Tanzania.

I'm an American who is curious to learn more about Africa.

I assume you mean Southeast Africa, since the Kenya/Tanzania region is different from the Horn. They're pretty different by virtue of being on opposite sides of the continent. The similarities are what's most interesting to me. But to answer your question:

1. West African languages are tonal, but most East African languages lost their tones. We share some of the same words, but the loss of tone is still there (E.g. Nyingi = mother in both Kalabari Ijaw and Swahili).
2. I find East Africans more laid back, while us West Africans are bolder (Nigerians and Cameroonians being the craziest)
3. All anglophone and hispanophone West Africans speak the same mutually intelligible Pidgin, but East Africans don't have a Pidgin of their own
4. West African athletes excel at power sprints. East African athletes excel at long distance running.
5. I feel East Africans are generally more politically conscious than West Africans, so more resistant to Western imperialism
6. West Africa has 9 French-speaking countries, East Africa doesn't have any
7. West African music is a lot more diverse and developed in my opinion
8. East Africa has better nature preserves. It's beautiful.
9. West Africans and East Africans practice Islam and Christianity, but I think West Africans practice their traditional spiritualities more—and those spiritualities have strong representation in the diaspora.
10. East African food is heavily derivative of South Asian food to me. West African food is more original and diverse to me.
11. Southern East Africans, particularly Kenyans, are a lot more liberal to me than West Africans.