Q:

Could Neolithic people outrun modern athletes?

I heard in many documentaries that people in the past had higher stamina due to the necessity to walk everywhere or because they worked in the fields. 
The Daily Mail reports: 

Mo Farah would have had some tough competition from ancient farmers living 7,300 years ago.
  Scientists claim if they were to cross paths, our ancestors would have been capable of outrunning some of the world’s most talented athletes. 
  That's according to recent research by Cambridge University which reveals just how far our fitness has fallen in just a couple of millennia.

But is that true?

A:

The statement is so vague that it could be technically true but mostly meaningless. It seems like typical mainstream media misrepresentation of science. Could some ancestors outrun some of the world's most talented athletes? Probably. A nomadic hunter could probably outrun a shot put champion, for example. However, I don't think prehistoric people with a time machine would sweep the 2016 Olympics.
The article in your question links to another article that is itself a misleading representation of the original publication from the University of Cambridge. The study found that bone density decreased following the agricultural revolution, which implies a reduction in activity. The original article makes no mention of stamina whatsoever. Here's the quote that somehow turned into prehistoric people outperforming professional athletes:

Using Shaw’s study of bone rigidity among modern Cambridge University
  undergraduates, Macintosh suggests that male mobility among earliest
  farmers (around 7,300 years ago) was, on average, at a level near that
  of today’s student cross-country runners.

I don't think it would be impossible to find a community today with conditions that are fairly similar to those of 7,300 years ago, at least with respect to physical activity. There are uncontacted people in various parts of the world who do not enjoy our technological conveniences that reduce stamina. Such individuals probably have better cardiovascular health than a person with a desk job who doesn't exercise, but I don't believe they regularly beat professional athletes, unless they are scouted and put through formal training.
Likewise, the average person from 7,300 years ago may have been in better shape than most non-athletes today, but I don't see any way that they could hold their own against modern people who have the luxury of building their lifestyle and diet around training for physical competition as well as 7,300 years of natural selection to their advantage.

