If a missile fails on the rail, that rail is out of commission until the missile is removed. If a missile fails in its canister in a VLS battery, only the missile is lost, generally. With VLS, you can keep firing missiles with less disruption do to the failure of individual missiles.
VLS eliminates the need to move a missile from the magazine to the rail, eliminating the time and moving parts required to move the missile. With VLS, you can fire missiles faster with greater reliability.
Not all missiles are the same. A VLS or a launcher magazine may contain anti-surface and anti-air missiles, as well as anti-air missiles of different capabilities. Rail launchers must "load" the required missile, a requirement that may change before the missile is deployed. With VLS, the entire battery of missiles is available.
The speed at which fire control systems operate to identify and engage targets is better served by the flexibility, speed, and reliability of a VLS rather than a rail launcher.
The rail launcher represents a single point of failure. Battle damage or other failures the render it inoperative necessarily deny the ship the remaining magazine. With VLS, the missile itself is the point of failure.
Since missiles are in self-contained units with VLS, it is easier to remove or replace missiles from the VLS battery than it is to remove them from the magazine the feeds a rail launcher.
It is easier, though not easy, to adjust VLS for longer, bigger, and more powerful missiles than a rail launcher and its loading system. With VLS, you have fewer constraints on future missile design.
As to why the US Navy decommissioned ships equipped with rail launchers, that decision has to do with maintenance concerns/costs and weapon system capability as well as life-cycle costs and mission capability of the ships themselves. The decision to decommission the Flight 1 CG-47 ships (Mk 26 launchers) was different than the decision to decommission the DD-963 ships that had been converted from ASROC launchers VLS, but that is a separate discussion.
Was it that much of an improvement? Was it impossible or that prohibitive to retrofit otherwise relatively new ships?