If an example of where there is a difference would help, consider these two possibilities:
To an egoist those two possibilities look about equally bad.
To those whose main concern is existential risk, the second option looks a lot worse.
I would call myself more of an egoist, and I would say the first possibility looks really good and the second possibility looks pretty bad. I of course assume that I am part of the 1%.
Many people on Less Wrong believe reducing existential risk is one of the most important causes. Most arguments to this effect point out the horrible consequences: everyone now living would die (or face something even worse). The situation becomes even worse if we also consider future generations. Such an argument, as spelt out in Nick Bostrom's latest paper on the topic, for instance, should strike many consequentialists as persuading. But of course, not everyone's a consequentialist, and on other approaches it's far from obvious that existential risk should come out on top. Might it be worth to spend some more time investigating arguments for existential risk reduction that don't presuppose consequentialism? Of course, "non-consequentialism" is a very diverse category, and I'd be surprised if there were a single argument that covered all its members.