It depends. For one-off activities, conducted in a faraway location, using public wifi can provide an additional layer of security. But depending on the location and how you approach it, this layer can be strong or week. The proper usage of public wifi can kill an investigation, especially into one-time activity that happened months or years ago.
Consider the following:
- There are cameras everywhere, that track people with facial and gait recognition.
- Your movements are likely tracked with your cell phone, and license-plate reading street cameras.
- Public wifi logs MAC addresses - so you would need to randomize that the least.
- Don’t forget the “classic” traces you leave behind - like footprints, fingerprints, DNA.
- In a public setting, you open yourself up to LEA storming you and performing a cold-boot attack, similar to what happened to Ross Ulbricht.
- If you’re actually in the place with the public wifi, you also risk the chance of someone just looking at your screen, and reporting you if it looks suspicious.
- Using a long-range antenna can mitigate some of the aforementioned risks.
The Hitchhiker’s Guide contains a lot of useful information on using public wifi.
The chances of a VPN getting deanonymized are far, far higher than Tor deanonymization. If your public wifi activity was uncovered, “they” (assuming a government in this case) would start an investigation and already know what general area you live in, provided the public wifi location was close.
That’s not how Tor works anymore due to guard nodes, which caps out the likelihood of getting de-anonymized circuits for each rotation period. Also all nodes are not weighted equally, relatively smaller nodes account for the majority of the bandwidth.
See: What are Entry Guards? | Tor Project | Support
Also check out this post: How probable a 3 compromised Tor relays? - #10 by Factorial
But don’t get me wrong, despite its weakness, tor is still very good, just not invulnerable against certain adversaries.