The "just sitting" practice is
shikantaza but I don't know how effective this is for attaining stream-entry. I think there may be more zen-orientated practitioners on here and KFD who could probably offer a better view on this than me since my own experience is primarily vipassana based. As far as I know, in shikantaza you're not really exploring as such, it's more that you're staying present constantly and bringing the attention back to the present moment over and over again. Again, I don't know enough about this so it's just an opinion based on my own experimentation with this technique.
I got the impression that "just sitting" had something to do with that sudden non-dual recognition aka. rigpa aka. many other words (satori? and kensho? a glossary would be nice).
Be careful of confusing your terminology here, satori and kensho aren't the same thing although the do reveal the same territory. I'd rather leave you to get information from someone more familiar with this system than I am as I don't want to muddy the water.
Advice? I can only speak from experience, but vipassana wins hands down for me. It's effective, precise and simple.