It sounds like you might be using the standard Text object. If so, that might be the issue.
Sprite Fonts vs Standard Text
If you use a Sprite Text object instead of standard Text object you should be able to get exactly the same result across all browsers. By contrast, the standard text object may not always get rendered as the same font from browser to browser, much less be rendered in exactly the same position.
The unpredictability of font rendering across browsers is not a bug in C2, as far as I know, but is just a side effect of different browsers all using their own method for rendering text.
By using a sprite font, you guarantee that C2 is directly responsible for rendering the text, directly from bitmap images, and so it will appear consistent everywhere.
Using Sprite Fonts
While it is a bit less convenient to work with Sprite Fonts, there are a few community made tools that make using them much easier.
Sprite Font Generator - v2
Sprite Font Generator is a freeware stand-alone font to sprite font conversion tool. It also generates all the JSON code needed by C2 to space and size sprite font characters, and it has a graphical interface.
Sprite font +
Sprite font + is a plugin for C2 that can take the JSON code for sprite fonts as a parameter, and will display (in the editor) the correctly sized and spaced character as they will appear at runtime.
Tutorial, for Sprite font +
Tutorial showing how to use "Sprite Font Generator" with "Sprite font +"
Hope this helps out.