I have both 4k and FullHD versions. And yes, it is faster but If you use it for just a regular streaming device, you can't find any noticeable difference. But this fire tv(4k) have the most powerful hardware. I use it for Prime video, Netflix and KODI. I have some highly compressed H.265 10bit AAC-LC FullHD videos on my Home Media Server which can't supported by the previous version of firestick. But this firestick can play it butter smooth, even high bitrate 4k/1080p 60fps videos.
I know it is bit pricey in india but I strongly suggest to go for this one even you have a FullHD or HD ready TV.
You can also check these link for any confusion
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Source
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Amazon Launches Fire TV Stick 4K: 4Kp60, Dolby Vision, Dolby Atmos, HDR10+
I hope you find this helpful. If have any doubts feel free to ask.
P.S: Some third party apps for pervious firestick will not work properly straight way but you can easily find the tricks on the internet.