So, there are 2 issues here:
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why does it look different (on IE it is bolder, more anti-aliased)
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how do I make the Mozilla rendering look like the IE one and what impact does this solution have (I am looking for minimal changes, so solutions such as – flash, silverlight or using images are out of the question)
Not exactly a “minimal change” but certain fonts and sizes look better/more consistent than others. I couldn’t say which combinations off the top of my head but I have noticed that some fonts render a lot more bold at 16px than at 15px for example. Experiment and you might find something you can live with. Alternatively try feeding a different font-weight to IE using conditional comments.