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What datasheets tell you, and what the comparator really does,
diverge a lot depending on the input slew rate and overdrive
level. A very low overdrive (one that does not fully steer the
front end) blows out prop delay big-time. Usually the Tpd test
will be at a sensible minimum overdrive and you can count on
the comparator being faster if drivenfaster / harder. But with
a slow ramp as shown, your delay at low overdrive can end
up looking like an offset term and somewhat hysteretic (even
if DC hysteresis is nil).
The graphs on the datasheets for the LM339 and LM393 comparators show 5mV, 20mV and 100mV override and the resulting different response times. It looks like the open collector output with a 5.1k load to +5.0V goes high (output transistor turns off) has about a 5 times longer response time than when it goes low.