It depends on the purpose of the lawn.
Peat based sod is for what we call the “classy” lawn or the “look but don’t touch” lawn. Peat based lawns are very high maintenance. They require vigilance and uninterrupted care. The benefit of a peat lawn is that it will achieve much darker colour than mineral based lawns. It will also achieve a much thicker, pillowy-soft density.
The drawback to a peat lawn is that it dries out very quickly. Two or three days of thirty degree heat will quickly stress the lawn. It is also somewhat more susceptible to insect problems and distinctively more susceptible to disease. Peat lawns also suffer quickly under even light or medium traffic. When properly cared for, peat based lawns look absolutely amazing; the key word being “look”. Just don’t touch. If you have kids or a pet, a peat based lawn is not for you. If you’re all about appearances and have a high appreciation for a beautiful lawn, you can’t get a better looking lawn than a peat based lawn.
As for mineral based, this describes virtually 100% of public lawns and parks. Mineral lawns can take a beating. The main benefit of a mineral lawn is clearly its durability. Mineral based lawns can easily withstand light to medium traffic which is why it is the sod of choice for sports fields, parks, and public areas. It is still susceptible to insect and disease problems, but less so than peat based sod. Mineral lawns can withstand longer periods of dry weather and neglect.
The drawback to mineral based lawns is that it can be difficult to achieve an amazing deep green colour. Mineral based lawns will never match the thickness, density, and texture possible with a peat based lawn.
If you have kids or a pet, mineral based sod would be the better choice.