The scenario is: John is out of home and, using his smartphone, he need to send some messages from Whatsapp, use Facebook's app and do some bank operations.
Since I have read this and this topics, I'm thinking about what is the safer option between 3g/4g (imsi-catcher threat) and public wifi (sniffers threat).
If John have both options, which one should he choose, and why? And what precautions should he have (tools are permited, but without root)? Consider John as a non-technical user.
If John have both options, which one should he choose, and why?
This depends on your threat model. Modern public hotspots do not use encryption or authentication whatsoever, allowing absolutely anyone with basic consumer hardware to sniff and modify unencrypted traffic. Cellular networks, on the other hand, do use encryption and at least a certain level of mutual authentication. Attacking it requires specialized hardware and often specialized cryptographic knowledge. While it may be possible to break 3G and 4G encryption, it's going to be far harder than just setting up Wireshark on a public network, which can be done on pretty much any laptop.
However, cellular networks are also very long-range, meaning that the data, potentially encrypted only weakly, is traveling very long distances. Compare this to Wi-Fi where the effective distance is quite limited. In fact, due to latency requirements in the protocol, there is a hard limit for active connections enforced by the speed of light. Passive monitoring must also be done locally due to the relatively low-power wireless transmissions made by Wi-Fi routers and computer wireless cards.
Overall, if your adversary, positioned on the airwaves with a transmitter and receiver with the intent of monitoring your wireless traffic, is local and unsophisticated, then Wi-Fi is dangerous. If your adversary is remote and sophisticated, then cellular networks are more dangerous. Note that WPA3, an upcoming encryption feature for Wi-Fi, will allow public networks to provide encryption even without a password.
And what precautions should he have (tools are permited)?
Use of a VPN to a trusted endpoint will protect from any relevant wireless attacks. A VPN creates an encrypted tunnel between you and a server, and that server connects to the websites you visit on your behalf. While VPNs are often advertised (incorrectly) as anonymity tools, they are actually only useful in this scenario for encryption. A VPN will ensure that an attacker who is able to monitor your wireless traffic will not see what sites you visit or the data you send to or receive from said sites. If you do not wish to pay for a commercial VPN or configure one yourself, Tor is a free alternative.
Assuming it's not possible to use any kind of encrypted tunnel, the next best thing is to only connect to websites that use TLS (HTTPS sites). Someone monitoring your wireless traffic will be able to see the website you connect to, but not what page on that website you are visiting, nor what you upload.
is there some sort of infection that spread by just being in the same network of a infected device?
It is possible in theory, and vulnerabilities in Wi-Fi chips have been found that allow for remote arbitrary code execution, but they are unlikely to be used as an infection vector for a worm. It is more likely to be used by a sophisticated attacker targeting one or a few specific individuals. If the Wi-Fi chip itself is compromised, it can often (but not always) compromise the computer's operating system. This can be partially mitigated by enabling an IOMMU. I believe Windows does this by default, to a limited extent. On Linux with an Intel CPU, you can enable this by adding intel_iommu=on to your boot parameters.
