They're actually complimentary. If you think about it, having a toll system without good public transit isn't going to reduce congestion very much for inelastic demand (eg. trucks going to deliver goods, people going to work) and is essentially a tax. However, when there is both a good public transit and a toll system, people can then pick between paying the toll or taking public transit.
The theory for toll systems is that by having a congestion charge, people will avoid using roads when they're congested makes sense, although it disregards several factors. Most people have to go to work between certain hours (which is why during rush hour the trains in Tokyo are crammed with people while outside of them they're not crowded at all) and that people often cannot relocate closer to work for various reasons (eg. children, unavailability of housing, etc.).
Furthermore, specialized white collar work (eg. software developers, lawyers, accountants, actuaries, etc.) often is only done in city cores, not in suburbs, meaning that people not living in the city core either have the choice to pay the toll or be underemployed.
As you mention, earmarking tolls to go towards improving public transit is a great idea; it will make the ratio of people paying tolls and taking public transit tend towards its equilibrium, as the more people deem public transit unusable, the more funds will go towards improving it.
There is an extra benefit for public transport. If people have to pay to drive, they will be willing to pay more to ride. The more users pay, the less it costs the public, and more of it gets built.
The theory for toll systems is that by having a congestion charge, people will avoid using roads when they're congested makes sense, although it disregards several factors. Most people have to go to work between certain hours (which is why during rush hour the trains in Tokyo are crammed with people while outside of them they're not crowded at all) and that people often cannot relocate closer to work for various reasons (eg. children, unavailability of housing, etc.).
Furthermore, specialized white collar work (eg. software developers, lawyers, accountants, actuaries, etc.) often is only done in city cores, not in suburbs, meaning that people not living in the city core either have the choice to pay the toll or be underemployed.
As you mention, earmarking tolls to go towards improving public transit is a great idea; it will make the ratio of people paying tolls and taking public transit tend towards its equilibrium, as the more people deem public transit unusable, the more funds will go towards improving it.