If Earth 2 has been producing noise for 200 years, that gives us an upper bound of 200 light years. However – for general terrestrial traffic – our detection range is only about 1 light year [1].
There are also no stars within that distance from Earth 1. So, at current levels of technology, Earth 2 would have to be a sad star-less frozen ball that just happens to drift into our neighbourhood within the appropriate 1 light year window on its eons-long journey.
Given that, I think we got the best deal here on Earth 1.
[1] https://physics.stackexchange.com/a/245562/4602 (the author does mention interesting caveats regarding directional transmissions though)
Edit: s/200 window/1 light year window/