Gaussian should be a much better approximation to the Bessel function, which is what you get with an ideal circular aperture (see attached plot). Is there no Bessel option in your deconv software? Exponential is very unphysical for any optical instrument, though it may be useful for removing pixel "bleeding" from CCD recorded images.
To my eyes the RHS images look much better. The bottom right looks best. I don't think you have lost detail there. You're just not adding detail that was not there in the first place. It seems to be the most artifact free (e.g. ringing at the limb).