Browsers, by and large, have different font rendering engines/methods. For more details, I recommend reading this, this, and/or this.
Honestly, to the average user, the difference will not be all that noticeable and for the most part, pixel-perfect cross-browser display of anything has been long abandoned as a print-world aftereffect.
If, for some masochistic reason, pixel perfection is more important than sanity and maintainable code, you can try the old standy-bys (text-in-images, image/text replacment) or turning off subpixel rendering via CSS (although not all browser support it, and the text will be less readable).
Hope that helps.
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