networking

A VPN is (in a generic, high level sense) a proxy. It's just proxying layer2 frames, vs. layer 4 protocols.

So the answer depends entirely on the traffic and the architecture you've built to support it.

Generally speaking it's possible for the performance to be essentially identical.

It's more important that you pick the correct tool for the job and the how and where it's being hosted makes sense for your use case.

Keep in mind that there's many forms of proxies and VPNs. So your question appears more like "what's faster, a truck or a car?" People would ask you if it's for highway driving, towing a boat, getting to work in the city, etc

So let's establish your use case. I'll give you a few examples that are in favour of various popular technologies.

If you're looking for something to run internally on your network to cache the internet to conserve bandwidth for all your clients. A squid proxy may be what you need.

If you're looking to hide from your ISP that you're using deluge to torrent Monster Musume a 3rd party VPN service (preferably using wireguard and a well reviewed provider) is more suitable for security and performance.

If you're in a country where you could be executed for posting doodles of Muhammad, you'll need a much more complicated suite of tools and the knowledge to safely use them.

https://youtube.com/playlist?list=PLQVJk9oC5JKp_8F9LPa3Pv67boA80KLm1

https://youtu.be/4A9MmnAz9Tk

https://youtu.be/88GyLoZbDNw

It all depends on the hardware doing the work and the configuration.

VPN will be quicker for some while a proxy connection will work for others.