Different search coils offer various benefits. Larger coils allow you to cover more ground and penetrate deeper into the earth. A small coil may get a little less depth but it will allow you focus your search in trashy areas to better separate trash versus treasure. Likewise, a smaller coil will allow you to search in tighter spaces (i.e. brushy or rocky areas).
A coil cover is a priceless investment as it protects one of the most valuable parts of your metal detector.