MacBook Air (mid 2013, 13", i5) - Geekbench scores on MacOS and Ubuntu
Why would that be?

Any number of reasons; however I would point towards testing methodology.  Looking at the Geekbench Score for a MacBook Air 11" Mid 2013, it got double your posted score and fairly in line with Ubuntu.

It's important to note that the score on the following chart are the "average" scores - meaning many higher and lower.


  To make sure the results accurately reflect the average performance of
  each Mac, the chart only includes Macs with at least five unique
  results in the Geekbench Browser.




Why the large variance?


macOS High Sierra, you didn't specify if you were using the latest updated version. 
One test was done with a live CD
The Ubuntu score is referenced directly (unlike the others).  What "tuning" was done, if any is not noted.
macOS will limit the amount of CPU available to manage temperature.  Ubuntu does not.


Those are just some of the possible reasons for the large variance and is by no means an exhaustive list.