At a level that the user doesn't have much control over, I fear both stock systems are about the same in terms of privacy.

According to an analysis by Köllnig et al. (2021) on 500k+ free Google Play/App Store apps, tracker libraries such as Google Play Services/Apple's SKAdNetwork/cross-platform libraries are used in about equal percentages on both app stores' free apps. These free apps' trackers are generally not configured to follow GDPR data-minimization practices, even for kids' apps, but it's to be noted that Android has a disadvantage in that advertising ID is more used in Android apps than Apple apps. However, Apple has disadvantage too: the researchers noted that Android's intent system and different permission model makes apps seem "more privileged" than Apple's, but Apple makes accurate analysis of their apps' reach difficult, judging by the larger failure rate in app decompilation as well as the more opaque approach to permission disclosure. Although the paper might imply Apple has improved over time, since it mentions Apple's implementation of opt-in tracking in 2021, after the study, as a limitation, keep in mind Apple's new movement towards advertising as a form of revenue, as discussed by Apple Insider (Owen, 2022) and Bloomberg (Gurman, 2022).

Of course, Köllnig's study only reflects tracking in "curated apps" for either platform. It does not discuss hardware/firmware/system app-level privacy, which users have little control over (Leith, 2021 -- easier reading with TomsGuide). Leith found that either OS phones home (lol) every ~4.5 minutes, and even though Google may send more data (even from the clock app!), Apple profiles your social network via MAC addresses on your Wi-Fi as well as location geotagging, which the TomsGuide article called "quality vs. quantity". This builds on the idea that Apple might seem more private, but only ostensibly so, judging by these more particular looks at their data collection and the trend of their increasingly data-focused business model.

Does that mean the choices between stock OS don't matter? Well, no -- as for me, who can't afford a Pixel anytime soon, I've chosen Android on account of freedom outside of curated app stores. Yes, PrivacyGuides may not recommend F-Droid, but the opportunity cost in security there may be negligible compared to the convenient and easily-handled privacy received in exchange*, at least for typical less-savvy threat models like my own. (This favorability is illustrated in a forum debate here (Lukas, 2023), though in a context less relevant to stock OS comparisons.) Ignoring the facet of freedom with stock Android, the possibility of large privacy advantage one way or the other, strictly in terms of stock Android and stock iOS operating systems, is marginal if it even exists.