For me (on Linux) the font is much prettier and much easier to read in Firefox. Firefox also seems to render it lighter than Chromium-based browsers.

Edit: I looks so different that I really thought it was falling back to a different font, but the Google Fonts page produces the same effect.

https://fonts.google.com/specimen/Cormorant+Garamond

On my Android (Chromium based browser) it renders very thin and dark as well. On Firefox on Android, it renders the same, but much lighter.