Anonymity cannot be guaranteed, but between the two options, the phone or reusable card based version is guaranteed to invade your privacy to a much larger extent.
At worst, a paper ticket can reveal your location when you buy it, when you start a journey, and possibly when you transfer or end a journey. It's already a close to ideal system: it provides proof of the right to travel in the event of a ticket control, without needing to reveal your identity, destination, past or future journeys, home address, phone number, banking details, or any other extra info. Out of band info exists in either case.
A phone app, which is what everything trends towards and seemingly what most people want to use, almost certainly has access to enough information from your device to uniquely identify you. The default will be to ask for your location, and most will grant it. Now the app knows who you are, where you live, exactly when you travel, who with, to what destinations, etc.
The trend is always towards more surveillance. Regardless of what is technically possible, digital will always struggle to achieve the levels of privacy and anonymity that are trivial with century old technology.
I grew up with the paper tickets, and remember being jealous of people with a Navigo. They could go through the gates so fast, and the contactless tech and little "bling" sound the gate makes when they touch in seemed so futuristic and cool! I never thought I'd come to see the paper tickets as almost too good to be true. That they have survived this long feels like a glitch in history, and in a rapidly evolving world they're a strong reminder of what's being lost.