No. Not really. It's faster and Apple touts "more better and bestest," but it's such a mild update to the 12 that if you are on a 12, there's no compelling reason to move... except for one: Cinematic Mode. This feature is available on all flavors of the iPhone 13 and, in basic terms, "pulls focus" automatically. This means, when enabled, the iPhone will focus to what it believes to be the prominent subject in a video. It's neat, and if you are shooting a lot of video with your iPhone it is a really slick feature. If you are interested in Cinematic Mode, definitely go for the iPhone 13 Pro or Pro Max to take advantage of the better camera set.
Now, if you are still on an iPhone 5 or 6, yes, you need a new phone. I liked the size of my iPhone 5 and for those like me the iPhone 13 Mini will fit the bill... or the pocket. In fact if you are on an older phone and need to upgrade, only upgrade to an iPhone 13. Don't go for a 12, 11, or another. As a general rule, when it is time to upgrade, go for the latest model, which is of course the iPhone 13 (Pro, Max, Mini, etc.).