Hi Francesco,
The grid size is pixel size, which is determined in ISCE processing, via the multillooking in range and azimuth direction. In order to reduce the grid size (for higher resolution), you could always try to use fewer looks in ISCE processing; at the same time, this will increase the noise level. So you would need to find a suitable compromise yourself, as it varies from area to area and from sensors to sensors.
PS methods generally use temporal and/or spatial filtering to beat down the noise, thus, has a higher spatial resolution; while DS methods generally use multilooking/averaging to beat down the noise, thus resulting in lower resolution. The strength of DS in MintPy is no temporal deformation assumption, thus, suitable for complex temporal behavior. However, if the full resolution is your most important desire, and you know that your study area has a simple linear deformation, ISCE + StaMPS would be a more suitable choice for you.
Lanari et al. (2004) proposed a method for higher resolution results for DS, but this is not implemented in MintPy.
Lanari, R., O. Mora, M. Manunta, J. J. Mallorquí, P. Berardino, and E. Sansosti (2004), A small-baseline approach for investigating deformations on full-resolution differential SAR interferograms, Geoscience and Remote Sensing, IEEE Transactions on, 42(7), 1377-1386, doi:10.1109/TGRS.2004.828196.
I hope this helps to clear,
Yunjun