What are the time/space differences between random.shuffle(x) and random.sample(x, len(x))? [duplicate]

This question already has an answer here:

• What is the difference between random.sample and random.shuffle in Python 5 answers

I often come across the need for "shuffling" a python list in a manner similar to using the sorted function, i.e. return a shuffled copy of the list without mutating the original.

I know one can shallow-copy the list and then shuffle:

a = [random.randint(1, 1000) for _ in xrange(100)]
b = a[:]
random.shuffle(b)

The functional programmer in me wants a solution that is not mutative (and fitting into a single readable line is a big bonus), and so I want to use the sample function:

a = [random.randint(1, 1000) for _ in xrange(100)]
b = random.sample(a, len(a))

However, nowhere in the documentation can I find clues as to whether this is a good idea in terms of costs, both time- and space-wise, asymptotic or constant factor.

The post What is the difference between random.sample and random.shuffle in Python appears to be asking a similar if broader question, but a) does not have an accepted answer, and more importantly, b) none of the answers provide any mention of what the relative merits are in terms of time/space.

So my question is: what is the time/space cost difference, preferably both asymptotic and in terms of constant factors, between random.shuffle on a shallow copy, and random.sample(x, len(x))?

NB I recognize the title is slightly inaccurate because it doesn't make explicit the fact that I want a comparison of random.shuffle(x) where x is already a shallow copy. This is purely because of a need for brevity.