Marble is a softer stone which can stain or etch if it comes in contact with certain substances (vinegar, lemon, juice, alcohol or oils). A sealer will generally take care of this problem, however it needs to be reapplied periodically to maintain the integrity of the seal.
Granite is an almost worry free surface that requires less maintenance. It requires minimal sealing. Granite is very hard and durable, and it is extremely stain resistant. You can put hot pots and pans over it and even cut on it (although not recommended as it can dull your knifes). Under normal use granite should not chip, crack or scratch.
Quartz/Engineered Stone is completely maintenance free and does not require sealing. However it is not as heat resistant as granite and special care should be given when putting extremely hot pots and pans over Quartz surfaces.