Fabric chairs are available with many more options than your average leather chair, they either can be cheaper or more costly, the feel is much different, and they can come in a variety of different colors and patterns.
Like leather chairs, fabric chairs can be designed to be durable, stain-resistant, and are generally easier to clean and maintain, though they still require an element of care. You may need to turn your cushions on occasion, vacuum your fabric, and use a specific cleaner or cleaning method to keep your chair stain-free, depending on the material.
Some tips with fabric chairs: Make sure your colors/patterns do not clash, decide whether you want a recliner, a chair with an ottoman, or a straightforward armchair.
Focus on what your chair will be used for and who will be using it. If, for example, you have young children, you may want to choose a more durable stain-resistant fabric, like microfiber.
