The space character in KaTeX fonts is a bit too thin. In KaTeX_Main-Regular.ttf for example, space is 250 units wide. Since cmr10 has (FONTDIMEN ... (SPACE R 0.333)), the space should be 333 units wide. For confirmation, 333 is the width given to the space and nbspace characters in the Type 1 CMR10 font distributed by AMS.

Is this a big deal? Not really. But it explains why (for example) the Cases screenshotter test output looks more cramped on KaTeX than LaTeX.