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They do not match because of the difference in timing conventions. You have that

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A=rho*A(-1)+epsilon

SGU treat A as an exogenous state and present the response to A. Dynare splits A into two states:

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A(-1)

and

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epsilon

Because of this, you are looking at different objects.

Thanks for the responses.

Doesn't this mean that actually the x_t SGU define has to be x_t = [k_t; log(A_{t+1})] rather than x_t = [k_t; log(A_t)] as it is on p. 758?

No. At time t, A_t is predetermined (because exogenous). A_t+1 is not yet know and therefore associated with an expectational error.