I prefer Imagick for resizing, making thumbnails or merging existing images. GD I use to create images dynamically like graphs and charts. As for you original question, consider the lifetime of the images. Will they remain viewable for extended amounts of time? If so I'd go ahead an generate thumbnails with Imagick and store them. If not, then go ahead an generate on the fly without saving a copy so you don't end up with a ton of unused image files cluttering up your server.
For example, on an intranet site you might have this weeks funniest picture where people can post snaps from their phone to catch funny office moments. Changes frequently, you might only want to save the top 20. Store thumbs of the top 20, generate the rest on the fly.
Another thing to consider is processing, if your server is a beast and it takes under .2 seconds to generate a thumb from say a 3mb image your not really loosing anything for the processing. But if it takes 1.1 seconds for the same task, your impacting usability at a noticeable level, you should either cache or generate permanent thumbs.
Another 2c...
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