This depends almost entirely on scale. At low scales a scanner is more cost effective and faster (due to effectively zero set up time and effectively zero time to switch object sizes or PPI). At larger volumes instant-capture is much
much faster. It's also possible to get higher image quality (though this depends heavily on which camera, lens, lighting, stand, and technique are employed; it's also possible to get worse image quality).
Institutions that do this at higher volume (tens of thousands or higher) have switched very heavily toward instant capture (industry term for camera-based digitization as opposed to scanner-based digitization). The reasons are:
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Speed, especially for like-sized objects
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Quality, especially for those looking to digitize at FADGI 4-star preservation-grade quality
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Handling, since instant capture does not require contact with the object
This is true of nearly all kinds of materials at such institutions, but film scanning especially has seen a dramatic shift. The Library of Congress, as one fun example I'm particularly proud of, is using two of our systems to do the final preservation scan of the Farm Security Administration negatives.
We've written an extensive
guide to modern digitization, largely aimed at institutions rather than individual photographers. We've also written a
digitization color accuracy guide that is pretty universal to anyone who cares about excellent color accuracy.