Welcome!
Could you share the SVG file with us? We might need to examine some things, especially the text.
Are the Linux system and the Windows system on 2 different computers?
From what I can tell from your screenshots, it looks like the text is larger on the Linux system. Although I would need to see the SVG file, to be sure. Can you tell us whether it is the text which is larger, or the light green rectangle background object is smaller. The green rectangle looks like it's the same size, but again, it's hard to be sure.
Look and see if the text is still text, or if it was converted to paths. If it's text, what kind of text - regular text or flowed text?
If there are 2 different computers, look and make sure that the font that is used is installed on both computers. If the Linux system doesn't have that font installed, then Inkscape is substituting a different font (maybe a bigger font).
That's my best guess, it's the font that's different. But if it isn't we will keep looking for the problem.
