Fixed CM fee or percentage: which gives owners better budget control?

I’m comparing a fixed construction-management fee with a percentage-based fee for a custom home, especially where allowances and change orders may evolve.

A fixed fee seems easier to budget, while a percentage might be more transparent if the scope changes. But I’m unsure how each structure affects the CM’s incentives: could a percentage fee make cost increases more expensive, while a fixed fee lead to extra charges through change-order administration or excluded services?

I’m more interested in practical contract safeguards. Which terms would you insist on: a clearly defined cost base, fee treatment for allowances and approved changes, an open-book budget, caps on reimbursable expenses, or written approval thresholds?

Sources for the current development:
PT.23.2 CCDC Construction Management Contracts
Construction Management Contracts: A Quick, Comprehensive Guide | Procore