Does iPhone 6S or 7 eat more storage than 5S?

I am potentially upgrading and would like to know if I get a 32GB 6S or 7 and the latest (and continually updating) iOS eats so much memory that it's better to get more memory?

I have a 16GB 5S which is useless, especially since I want music to listen to offline.

Hope that makes sense!

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