> When resizing a transparent GIF the resulting image's quality has degraded

You have uncovered a bug.  The bug is fixed in ImageMagick 6.2.9-4 Beta
available sometime tommorrow.  Take a look at 

  http://www.cit.gu.edu.au/~anthony/graphics/imagick6/formats/#boolean_trans

which discusses how boolean transparency within the GIF image format is
problematic.  With ImageMagick 6.2.9-4 we got best results for your image
with

  convert logo_aladdin.gif -resize 300x300 -channel a -threshold 50% logo.gif
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