The main differences between hardneck and softneck garlic are between the climates where they grow best, and how well they keep in long term storage for use throughout the year.
Softneck garlic thrives in areas with mild winters, so if you live in USDA zones 8-12, this is the type of garlic for you. I live in 8b in the PNW, and I am able to grow both varieties successfully.
Hardneck garlic has fewer cloves, but each one is larger.
Hardneck garlic cloves have a thin layer of skin, so they are easier to peel than softneck garlic cloves.