In a comment, I mentioned that a modern cell phone could do almost everything the Saturn V instrument unit could do. How true is that? In particular, which would provide more accurate data for an inertial navigation system: the Saturn V's ST-124-M3 platform or an iPhone 13's MEMS accelerometer and gyroscope?
The ST-124-M3 platform wins, hands down.
The ST-124 was flight tested on the Saturn I flights. I found the corresponding test report "SATURN I BLOCK II GUIDANCE SUMMARY REPORT" from February 23, 1966 (link to PDF on ibiblio.org). The abstract reads:
One of the missions assigned to the Saturn I Block II vehicles was flight testing the ST-124 inertial guidance system. This is an analytic report of the ST-124 platforms and associated hardware flown on the six Saturn I Block II vehicles, SA-5 through SA-10.
This report presents for each vehicle the velocity component errors versus time for the total powered flight, combinations of platform system errors that would produce the velocity error profiles, and the velocity component error corresponding to each platform system error.
The results are in section 4.2 (p. 17), in particular table 4-III on p. 21 that reports constant and g-senstive drift, which are performance metrics for gyroscopes and IMUs. The table reports constant drift in the order of 0.1 deg/hour and g-sensitive drift (g as in "9.81 m/s/s") in the order of 0.1 deg/hour/g.
In contrast, this recent overview article on MEMS gyroscopes and IMUs (2020) reports that:
“Today, 1 to 5 °/h is feasible with MEMS. For the future, the range below 1°/h seems accessible.”
Specifically for the iPhone in the question: an iPhone 13 disassembly revealed a Bosch Sensortec 6-axis accelerometer/gyroscope. The datasheet only reports g-sensitive drift, but it's 0.1 deg/s/g, about 3600x worse than the ST-124.
The ST-124 was an order of magnitude better than the best MEMS IMUs today. It also weighed 48 kg and used 187 Watt, so not really iPhone-compatible...