If you want to check if two arrays have the same shape AND elements you should use np.array_equal as it is the method recommended in the documentation.
Performance-wise don't expect that any equality check will beat another, as there is not much room to optimize
comparing two elements. Just for the sake, i still did some tests.
import numpy as np
import timeit
A = np.zeros((300, 300, 3))
B = np.zeros((300, 300, 3))
C = np.ones((300, 300, 3))
timeit.timeit(stmt='(A==B).all()', setup='from __main__ import A, B', number=10**5)
timeit.timeit(stmt='np.array_equal(A, B)', setup='from __main__ import A, B, np', number=10**5)
timeit.timeit(stmt='np.array_equiv(A, B)', setup='from __main__ import A, B, np', number=10**5)
> 51.5094
> 52.555
> 52.761
So pretty much equal, no need to talk about the speed.
The (A==B).all() behaves pretty much as the following code snippet:
x = [1,2,3]
y = [1,2,3]
print all([x[i]==y[i] for i in range(len(x))])
> True