The effect they have on the format? Let me tell you the effect Combo Winter had on the format. For the first two months there were literally 2 playable decks in Standard. Academy decks, and merfolk decks completely packed with anti-Academy hate, including four Academies of their own because of the old, old Legend rule. In fact, there was a playset of Tolarian Academies in literally every deck that was even a remote attempt at competitive, regardless of whether they played blue or any artifacts.

As an aside, dismissing how fast a deck can "goldfish" as being unimportant doesn't make any sense when you're talking about a turn 1 kill in a format with no free disruption. It's extremely relevant if you can sit down to a game and lose without ever having an opportunity to do a single thing.

Anyway, that was the first two months of Combo Winter. They banned Academy (and Windfall), and the format diversified to about 4 different turn-2 and turn-3 combo decks, including the Academy decks that only got slowed down by about a turn after losing two cards to the last ban. Again, it's extremely relevant if decks can goldfish turn 2 kills if the only counterplay you have against it is to aggressively mulligan for Force Spike or Duress to try to buy an extra turn or two.

After another banning round neutered all those decks, Memory Jar showed up with yet another deck that could pull off turn 1 kills in standard, even after a mulligan to 4.

If you want to talk about the effect on their respective formats, the Eldrazi deck is so far away from the series of circumstances that led to Memory Jar's emergency ban that there's no comparison.