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Some scanners aren't just aimed at the domestic market but for the professional market too, where the likes of advertisers, for instance, need super high resolution images for marketing billboards etc.
Have you checked the canvas size of the negatives you scanned, by that I mean what size print it would produce if you were to use every single pixel? I am sure you would find it was massive! Now when you shrink down the size of that canvas to a more manageable size a printer can only reduce each of those dots down to a specific size because of the limitations of the laws of physics, hence if you were to print this file at 300dpi, just like a jpeg discarding the information it didn't need, your printer software would do the same thing. The difference though is your eye wouldn't be able to see any difference on the final print. Now if you compare one of your scanned negatives saved as a Tiff against one saved as a jpeg, both scanned at 600dpi and you will see a diiference in the tonal values saved in each, because one will show as an accurate representation of your scanned negative, while the other will look like it has been adjusted. Which is precisely what has happened.
Now to answer your question as whether 600dpi would look the same as 300dpi depends on two critical elements. The first is the size of the print and the second is from what distance are you going to view the print. Well you've mentioned the size would be 16 x 12, which you could print sucessfully at about 250 - 280dpi and the image would be perfectly crisp as you gazed at the whole print from a comfortable viewing distance. However, if you were to scan an area of the image with a magnifying glass it may not look as good, but that's not how you're really going to look at it. Now if that image was printed at 600dpi it would look better under a close inspection, but from a distance our eyes wouldn't tell the difference.
So the dpi required is only relavant to the size of the canvas we are going to print it on. The larger the canvas, the greater the dpi has to be to achieve the required quality, but you don't have to go to extremes!
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