Has anyone been to either the Azores or the Canary Islands? Worth a dedicated trip?

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Canary Islands are an archipelago compound by 7 Islands quite different from each other. Unless you have a work+visit plan I would not recommend seeing 7 Islands in a rush.
I've never been in Azores but Madeira is great, a mix between Canary Islands and Galicia

Central part: Main Islands
Tenerife and Gran Canaria share the Capital of the Islands.
Tenerife has 2 small cities and the Island is dominated by Teide. Black sand and white sand beaches, forest and desert. 
Gran Canaria also has forests and beaches and the biggest city among all islands. Big theme parks and hotels