In terms of the number of legal suits against them, home inspectors probably have a greater likelihood of being sued. Home inspectors have become the lightning rods of the sales transaction process. We live in a society where few want to take responsibility for their actions. It's easy for a buyer to blame the home inspector for any and all shortcomings in a property they have just purchased. On the other hand, inspectors can limit their liability by using a contract which, if well written, clearly identifies the limitations of an inspection and therefore the limits of the liability.
Many contracts actually limit damages to the cost of the inspection or some other fixed amount.
Appraisers do not operate under any such contract. Finally, suits against inspectors are usually for smaller damage awards than appraisers. Most claims are initiated because the inspector failed to clearly report a condition that the buyer discovers later. Appraiser suits can be in the hundreds of thousands of dollars and may be followed by criminal action or licensing sanctions. The truth is that there is plenty of liability in both professions.