This reaction and similar ones involving strong acids go almost to completion. Cl- is the conjugate base and H3O+ is the conjugate acid. A reaction will always go strong --> weak. That's how you know H2O is a stronger base than the Cl- base.
Re: negative charge. Just because it has a negative charge doesn't necessarily mean it's a stronger base. NH3 is a stronger base than any of the negatively charged conjugate bases of strong acids because of its lone pair of electrons. The same thing can be said for H2O.