You have to be careful comparing the same part number between manufacturers. It just means
most specs are equivalent, some worse, some better, some omitted.
The AP431 seems obsolete, replaced by
AP431S- which still has no aging, noise specs.
Diodes Inc. parts have been trouble for me in production, I no longer use them. They are cheap for a reason.
The TL431 (die pics and
some reverse eng) has different design priorities compared to a precision reference.
It seems to have higher gain, higher shunt current range, lower accuracy and no aging or noise spec. - it is better suited for regulator applications IMHO.
Cheaper voltage reference IC's are using EEPROM-registers for trimming, instead of laser-trimming.
On-Semi LM4040, LM4041 "... ON Semiconductor’s Charge Programmable floating gate technology ensures precise voltage settings offering five grades of initial accuracy; from 0.1% to 2%" {sounds like eeprom to me, like in TI LM41xx}
TI LM4040 "... uses a fuse and Zener-zap reverse breakdown voltage trim during wafer sort to ensure that the prime parts have an accuracy of better than ±0.1% (A grade) at 25°C" But even these have
changed with time.Assuming OP has a trimpot for A/D calibration, we don't care about initial accuracy, just stability.
If ICL7135 is fed 1.0000VDC ref, I wonder if going up to say $6 is worth it, compared to the resistor's trimpot/voltage divider drift and tempco.