Very very strong recommendation: get one eye done and wait a month or more before you consider getting the other done.
They will recommend you get both done at once.
Reason for recommendation: it is the only way to give yourself a before/after objective comparison between the operated eye and an native unoperated eye. If you get both done at once you lose all perspective (groan). Also one at a time lowers your risks a little I think.
I got one eye done years ago, and have kept using a contact lens in the other (never operated on). I was not thrilled with the stellation, which you can only objectively judge if you have one unoperated eye. Using a contact lens is annoying, but the option of not using it gives me some extra superpowers.