I don't have an answer, but just a possibility. Does the LaTeX document specify a specific font? If so, it's possible that the font is available on only one of the computers and on the other it's reverting back to a default font that looks similar but is of lower quality.
This would be indicated in the log file. Actually the log file is something you should check, anyway, since it may indicate some other difference that's causing the problem. So I would do a diff of the log files on both computers to see what the differences are.
If it's a font substitution issue I would expect the documents to have some other subtle differences, e.g., fonts having slightly different widths and kerning so that the lines in the document break between different words, or a line in one document runs slightly longer than the same line in the other.
Also, if it's not just text, but also images, that are the problem, then it's not font substitution that's the problem. In that case comparing the LaTeX log files should reveal differences.a