Analytic Tool: Mixpanel, Amplitude or Segment

Hi there!
We have a software product which and it is not a SaaS. It should be installed on the client infrastructure. I want to get to analyze user activity. I don’t want to use Google Tag Manager, because I didn’t find an option to write events from a server-side.

I am looking at Mixpanel and Amplitude. Can’t see much difference. I see that Segment is a really popular tool to use together with Amplitude, but I don’t understand the use-case.

Does anybody have an experience of usage Mixpanel, Amplitude or Segment?