+ VanitarNordic
It was Interesting to read your OP about the performance of voltage regulators versus precision references. So I did the comparison table below, showing the AMS AMS1117-3V3 and Microchip MCP1501&-3V3 to see how they looked side by side.
The chips are around the same price from first-tier suppliers. I used the latest AMS data sheet for the 1117 which seems less optimistic than the data sheet you quoted, but all the same the 1117 still came out well.
The bottom line is that if you want a reasonably good, comparatively high output current, reference voltage go for the 1117. But if you can get by with a lower output current go for a dedicated voltage reference chip and get a much more accurate initial voltage and more stability.
By the way, the 1501 data sheet is superior to the 1117. I had to extrapolate some of the figures for the 1117 from graphs and there was no indication that the graphs were typical, worst-case, or what! My impression is that the performance of the 1117, as a voltage reference, would vary quite a bit between individual devices. They are still great little voltage regulator chips though!