Last week I asserted that all else equal a user would choose the more private product.
But a friend pointed out that's not nuanced enough.
In practice, people also pick which product to use based on the expected rate of improvement, as well as the current quality.
Products that are less private have more data to use to improve the product.
There's more signal to aggregate and use to improve the quality of the system and prioritize fixes.
This could mean that a more private product would lose, all else equal, if users thought that the less-private product would improve faster.
However, in practice it's possible to get enough data to use to improve the product within conservative differential privacy limits.
The vast majority of non-private tools collect many orders of magnitude more data than they need, "just in case", and then do very little with it to actually improve the product.
All that data sitting there is just waiting for an MBA or finance bro to propose doing something with the data to make a quick buck.