That is the result of the way font rendering and SVG display works.
You may be able to improve the situation by using a font that is available on both machines (and measures similarly on both Windows and Linux).
Technical explanation (i.e. the gory details)
Currently, you have set the label font to 'Dialog'. However, 'Dialog' is not a real font but a symbolic name that is only available in Java applications. When you open your SVG document in a browser and the browser has to render text elements with font 'Dialog', it will not be able to match that font name with any existing fonts on your machines and use a fallback font instead. However, a different font also means a different text width and thus the text no longer appears centered.
You can verify that it is a text rendering issue if you set an actual border or background color for e.g. the "<<abstract>> Facade" label. Since label size is by default determined by the size of the text plus a 2px margin, this essentially visualizes the text bounds. If you open the corresponding SVG document in a browser, you will notice that the colored bounds are still centered in the node, but the text has changed in relation to said bounds.
To make matters worse, it is not even guaranteed that two different applications render text the same size even if the same font is used. I.e. a Java application may render the text differently from Firefox and Firefox may render the text differently from Chrome - even on the same operating system.
Finally, Linux usually renders text slightly larger than windows (even when you use the same font). Thus even if you use a font that is physically available on all the machines you view your SVG document on, the result will almost certainly slightly differ if you view the SVG document on the "other" operating system (i.e. the one the document was not generated on).
None of the above is actually a yEd short coming.