It sounds like you are experiencing expected behavior. The image you linked to looks completely normal (OSX on the left and Windows on the right). Windows and OSX render fonts differently, and most typefaces appear heavier on OSX. For instance, compare the weights on this page (under the ‘Browser Samples’ tab): https://typekit.com/fonts/chaparral-pro
I think you said it best yourself:
Im not referring to the different way OS’s handle antialiased text but a core difference in the way the font is rendered.
You have basically answered your own question without realising it. The different OS’s (and browsers) use different rendering engines, that’s just something we have to live with! Webkit has a font-smoothing property for text, whereas Firefox does not.