What they're genuinely great at
Asana is excellent at dependencies, ownership and keeping a multi-person project honest; Starter runs around $13.49 per user per month. Monday.com's colour-coded boards get adopted by non-technical teams faster than almost anything else, at about $9 per user per month with a three-seat minimum.
Both do the genuinely hard thing: making work legible across people who don't sit together.
Where they fall down
The unit of both products is the project, not the day. Your personal Tuesday is an implementation detail that neither tool models. And the three-seat minimum tells you plainly who Monday is for: it isn't a person.
How Fuidzy is different
The unit here is a day, and the shared version is deliberately small — a couple, a study group, a two-person company. Nobody gets a dashboard of anybody's productivity. What you share is when you're busy and, if you choose, what you're doing.
Use Asana or Monday if you have a team, a manager, and deliverables with dependencies.
Use Fuidzy if you have a life, and the coordination you need is with two or three people rather than twenty.