They are both just record-once DVD disks for a DVD burner/writer. They are meant to behave like regular DVD disks once they are burnt.
The main difference for their their use is that some older set-top DVD players can only read one kind.
There are other technical differences, but the only reason to choose one over the other is if your set-top player or your burner only works with one kind, otherwise just get whatever's cheaper/more available/comes in cool colours
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Like CookieRevised stated, they are both used as much as the other; they are designed to achieve the same goal anyway.
linx05 mentioned using Verbatim DVD+R for double layer burning because these disks are usually of high quality, while others are low quality or varying quality.
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