The best way to describe it is not by knowledge, but freedom. The people who were sent to Mars were not all "scientific minds". There were some normal people (as seen in the current Mars colonization efforts), but these people were easily manipulated, as seen in how the "knights" swore loyalty in return for Aldnoah, and thus suppressed the masses.
The people have no freedom. They are starving, eating krill to survive (refer to the scene where Count Saazbaum eats chicken for the first time), so the recent scientific advancement since the 1980s has not been "learned" nor "taught" to, or by these people. Instead, it has been kept under wraps by the knights and "king". This is why Princess Asseylum wishes for peace between Earth and Vers, so that the people no longer suffer without knowledge or freedom, so that a trade route for both can be obtained and thus the people can be "happy".
So to answer the question: Ver's knowledge is a lot better, but it is not as effectively used, as there is no fresh thought or freedom of thought.
If "knowledge = power", then the people have neither.