The verdict
If your problem is ownership and deadlines across many projects, pick Asana. If your team already keeps its docs, projects and decisions in Notion and wants agents and meeting notes there, pick Notion AI.
I would not buy Notion AI to solve a task tracking problem, and I would not expect Asana to be a wiki. I moved a team from Asana to Notion, mainly because we needed a knowledge base and flexible content management next to tasks. That was about consolidating tools, not about Asana failing at project tracking. If you are not on Notion at all, Asana is the simpler decision.