What's the difference between Segment and Mixpanel?

I didn't use either of these tools in my last app (to be honest, I'm not even sure they existed at the time). This time around, I want to make sure I'm leveraging the latest and greatest for analytics.

Would I use both of these at the same time or are do they overlap in functionality?

I've also heard of Amplitude as a competitor to Mixpanel, what would be the analog to Segment (or any other big ones I should consider)?

Thanks!