This comparison is a little different: Zotero isn’t really a competitor. It’s the best free, open-source reference manager there is — and Fynman imports directly from it.
So the honest answer to “Fynman vs Zotero” is usually both. Keep Zotero to collect and organize your references; add Fynman to do the things a reference manager doesn’t — gap analysis, cross-paper synthesis, and drafting — over that same library, on your device.
One thing worth knowing: Zotero’s free storage caps at 300MB (~100 PDFs), which nudges heavy users toward a paid storage plan. Here’s how the two fit together.