I would suggest opening up developer tools and inspecting the CSS properties being used. In theory, you should be able to get the font rendering to be the same. I’ve had issues with line height, but that’s something different. In your screenshot, it does look like an issue with color and font-weight, both of which can be overridden.
If you do not know how to use developer tools, here’s a post that’s helpful https://forum.obsidian.md/t/getting-comfortable-with-obsidian-css/133