I lean toward the first option for the following reason: I doubt that physical processes can be simulated precisely by a Turing machine.

For example, if I'm living in a simulation and I move my hand an inch to the left, it occupies an uncountably infinite number of intermediate positions during that motion. A Turing machine can't calculate or even represent all of those positions, since the set of Turing-computable numbers is only countably infinite.

Of course, what I've written above assumes that spacetime is continuous. Is it?

That can be tested by experiment:

https://physics.stackexchange.com/questions/9720/does-the-pl...

According to that link, spacetime shows no sign of discretization down to fourteen orders of magnitude below the Planck length. (The Planck length itself is so small that if an object that size were expanded so as to be a millimeter across, then a proton, at that scale, would be larger than the distance between the sun and Alpha Centauri.)

That suggests to me that while Turing machines can provide useful approximations to the behavior of physical systems, they can't represent or simulate them precisely.