Difference is subtle but outcome significant. When iterating over people - everyone will often think about themselves and what they have to do today. When iterating over tasks - everyone is involved in common goal. You are focusing on tasks needed to be done to complete the sprint. Few times already, during former type of standup, I've experienced repetitive answering the same questions everyday. People stopped caring about them at all.
Standing up was a specific solution to a specific problem. There may be other ways to achieve the same thing, but you should be aware of what you're doing.
> Your standup should be about tasks, not about people. The difference is subtle, because it the end everyone should share the same info - progress, blockers, etc. But by checking on tasks the team members automatically build mental model of current iteration. How far are they? Is the tempo OK? Or maybe there's some delay and, finally, can they deliver on time?
This really doesn't seem such an important distinction. You assign tasks to people in your iteration planning; if a task is stuck it will be because a person is stuck on it and vice versa.