The only advantage inherent in the Floyd Rose system itself is that it is "double locking". This simply means the string is locked at the bridge and the nut.
With non-locking tremolo systems, the string has to pass over or through potential pinch points both at the bridge and at the nut. String-through the body bridges can have 2 or more string bends at the bridge end, and most guitars without angled headstocks have string trees between the nut and tuning machines.
The impact of all of these points of contact is that strings can have friction at one or more of those points, which means the tension on one site of the friction point can be higher or lower than the other side. When a non-locking vibrato tailpiece is used, the tension on the sounding length of the string can be dramatically changed up or down, and the string can be pulled more to one side or the other at one or more points of friction. Once the tailpiece is returned to the neutral position, the strings can be displaced slightly and their tension on the sounding length can be off, which means they are now out of tune.
One popular strategy to prevent this is to reduce the friction at as many of those points as possible. This is the business that Graph Tech is in. They made their name by manufacturing self-lubricating nuts, bridge saddles, and string trees, that combined with locking tuners were marketed to prevent vibrato bridge use from throwing the strings out of tune.
The Floyd Rose solution is to prevent the string from moving at all across these friction points by locking the string in place at both ends of the sounding length. This means the locking nut keeps the string fixed at the nut end and the locking saddles in the bridge keep the string fixed at the bridge end. This means the sounding lengths of all strings are kept the same - the strings will not slip across the nut, string trees, or bridge, because they are locked in place. When you dive bomb with a Floyd Rose and then return to rest position, the strings will have the same sounding length and tension as before the dive bomb.
In case it's not clear, the primary disadvantage of the Floyd Rose system is that tuning up the guitar and changing the strings is more tedious and time-consuming. There are fine tuners at the bridge that work for tuning adjustments before in response to changing weather, but when you really need to fix the tuning of a string, you have to unlock all the strings at the nut, do all the tuning like normal, then lock the strings down again and fix minor tuning issues caused by the locking.
