Greetings from RojoLand!
Either of those machines would do the job (I have an A-4010S — never heard of an "AC" model — and I also have a Sony TC-730 which is a TC-580 with a built-in stereo amp and speakers), with a couple of caveats: The tapes you want to play back would have to be quarter-track, as both these machines are quarter-track stereo decks. Older tapes might be half-track, or two-track stereo. Such tapes would play on a quarter-track machine, but not optimally. Do you know approximately how old these tapes might be? Or, particularly, at what speed they are recorded? Generally, you'll find either 7-1/2 or 3-3/4 inches per second (IPS). Both machines can run those speeds, but if the old tapes were made at 1-7/8 IPS you'd have to go with the Sony.
Of the two, the TC-580 is a bit newer and offers more features (bi-directional play and record, for one, plus three-speed capability), but the Sony machine can be fussy and hard to maintain. I waited 37 years to find parts to fix my TC-730 (couldn't get 'em from Sony even back in 1981!).
Good luck,
—
J. E. Knox "The Victor Freak"