I think the only things I've heard that Uber copied off Lyft was multiple stop requests and in app and tipping. Otherwise it's the copycat Uber and some pax just say they prefer Lyft's customer service or believe they are cheaper/pay us better.
Uber was a black car service. Lyft came out with the cheap rides. Uber x was born shortly after. Lyft was coming put with shared rides(line). Uber scrambled to come up with and release pool. One company cuts rates so does the other.