Type 2 is far more dangerous at scale. Type 1 requires access to the agent interface — it's limited to insiders and session hijackers. Type 2 requires only the ability to put content somewhere an agent might read it. A single poisoned webpage can silently redirect every agent that fetches it.
In both cases, the agent's planning loop ingests attacker-controlled text and treats it with the same weight as legitimate instructions. The attack isn't a bug in the agent — it's a consequence of how agents work.