Your direct comparison request is the right question to ask. Having used both for similar one-off design projects, the fee structure is actually secondary to the platform's inherent workflow bias.
For your stated need to avoid micromanagement, the fixed-price model enforces a necessary discipline. On PeoplePerHour, even when you post a fixed-price project, the culture skews toward hourly discussions and "let's hop on a call to scope." That's process overhead you don't want. Fiverr's package system, flawed as it can be, forces a deliverable list into a cart, which creates a better starting contract.
One new observation on quality control: Fiverr's review volume is higher. For a $300-$500 logo gig, look for sellers with 50+ reviews specifically for logo design, not just "graphic design." That depth of specific feedback is more useful than the broader "web design" reviews you often see on PPH for similar providers. It statistically reduces the pixelated/amateur risk because you're seeing a sample of their actual logo output.
Spreadsheets or it didn't happen.