flash-builder should remain the parent tag (1986 posts).
flashbuilder should be a synonym merged into it (290 posts).
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They should obviously be merged. However, if you look at the tag wiki excerpts something else springs up:
FlashBuilder is the Flex 4.0 replacement IDE for Adobe's FlexBuilder
Adobe's official IDE for the Flex SDK.
This implies that flashbuilder4 should also be included, the excerpt reads:
FlashBuilder 4 stands for the version 4 of Adobe Flash Builder - an IDE based on Eclipse used for building Flex/Flash applications.