Not the same condition, only similar condition.
I recall reading about a statement in a textbook (unfortunately, couldn't find the source now) saying the change from disorder state to ordered state is always faster than the other way around, an example is melting is faster than solidification.
So, let's suppose two identical copies of a system, both at identical conditions: a phase equilibrium at $(T, P)$ between solid and liquid (of a certain substance).
- In copy A the environment temperature is increased to $T + \delta$ (so melting occurs)
- In copy B the environment temperature is decreased to $T - \delta$ (so solidification occurs).
Do both have the same rate of phase transition (measured by, say, moles per minute)? Thermodynamics does not tell rate of change.