It's not just about web search though -- there's another element too. I go to Grok to find things I have failed to find with web search.

I agree with GP -- if I want sourced commentary on current events, Grok is my go-to above the other models. For whatever reason, its search feels better and more up-to-date -- whereas the others feel more like filters of media, Grok feels more like filters of sources.

Could just be my perception though. YMMV

Grok seems to work faster, and especially in the context of twitter it actually is routinely used, and pulls from current events quite quickly.