If the citizen (as you say) is deciding between paying taxes or buying transit tickets on a monetary basis, he or she will choose the cheapest option, and the city will lose out on revenue. On a purely financial basis making this the citizen's choice cannot be a win-win for the citizen and the city.
Besides the above argument, it is also unlikely that there is any possibility of net revenue to the city. Even if a few people irrationally decide to pay more taxes than they were paying in transit fares, and hence generate some revenue, there are presumably only a small minority of the population who make this decision. But these additional tax revenues have to cover not just what these citizens were spending on their own transit passes, but also the loss in revenue to the city from everyone else in the city not paying for transit anymore.
Certainly, it is likely that free public transport enhances the economy and generates revenue in other ways, but it does not add up in the way you have presented it.