No, it's got nothing to do with whether the LM1458 or LM339 is used, it's purely because the second circuit is driving an RS flip-flip.
Do you know what an RS flip-flop does?
If not, I suggest you research it and you'll probably realise why you don't need a comparator with hysteresis if it's activating a flip-flip.
EDIT:
Here's a link to a circuit I designed for someone, which uses a few comparators to trigger a comparator based flip-flip. Note the LM339 and the lack of feedback resistors.