I think this article sums it up well:
The decision whether to use VPN or Private Relay comes down to:
- Does Private Relay provide the protection you want, or do you require a proper VPN?
- Does Private Relay work with all your key websites?
- Does Private Relay protect the apps you use, or do you use a third-party browser?
- Can you put full trust in your VPN service, its operator, and the jurisdiction from which it operates?
If that’s what you’re trying to do, iCloud Private Relay should do the job.
From Apple’s whitepaper:
Private Relay’s design, combined with a minimal logging policy, ensures that proxy logs do not contain enough information to connect a user’s IP address or account information with their browsing activity.
The information logged by Private Relay contains no unique identifiers and is limited to the following, for the sole purpose of operating and improving the service:
• Connection properties and performance metrics• Network and region information derived from IP address
• Anonymous token validation success rate and performance • Private Relay system resource usageThe following fields related to anonymous token issuance are logged as a part of Private Relay’s fraud prevention and anti-abuse measures, but cannot be correlated with connection information:
• iCloud account, software version, and request timestamp