So I rewatched episode 1 of Eureka Seven to see how close it mirrored up to Captain Earth and it's pretty damn close.
The speech with Daichi's counselor is pretty identical to the speech Renton got from his counselor. In both scenarios, Daichi's and Renton's father is viewed as a hero/celebrity and their guardians both flat out reject their ward following in the path of their father. You then later have this scene:
There is a sense of isolation from both and a discontent from both main characters about their futures. They both have their hobbies, that they're good at, but nobody takes them seriously and just view as them goofing around. There is also the usual boy meets alien girl that is (probably) the main romantic interest
This is much more common so I doubt it's a throwback to Eureka Seven and more of a general mecha trope, although Daichi's jacket when he was a kid is very similar to Renton's.
Why are you so mean, Jarmel? Firstly, comparing
Captain Earth to
Eureka 7 is some kind of cruel punishment because a direct comparison would reveal just how bad
Captain Earth is in comparison. You're right to say they share a handful of plot similarites, but a number of those are two do with BONES appreciation for the original
Gundam series which laid many of these tropes out e.g. our hero is a mechanic, slightly disenfranchised perhaps, adults are bad, and he's gonna end up in a robot by the end. The only real change from that is throwing a girl in there.
When you actually pull away from the macro level and look at all the detail you see why they aren't comparable at all. Pacing, script, direction (and tone), storyboarding, even art and animation. They're literally worlds apart.