Frequency modulation and phase modulation are physically equivalent.

Suppose you have unmodulated sinusoidal signal, '''e^w t^'''

This signal has the phase of

 . '''phi(t) = w t,'''

and frequency of

 . '''f(t) = 1/(2 pi) * dphi/dt = w/(2 pi) = f0.'''

Now we apply the frequency modulation with frequency deviation of df and modulation frequency of fm: 

 . '''f(t) = f0 + df Cos(2 pi fm t)'''
 . '''phi(t) = Integrate[f(t) dt] = w t + df/fm * Sin(2 pi fm t)'''

Now think about the phase modulation with modulation depth of m and modulation frequency of fm:

This means that the effect of FM is the same as that of PM. This indicates that the modulation depth of FM is given by 

 . '''m = df / fm'''.

For given df, FM gives a larger modulation depth with a lower modulation frequency.