Is the supplication, "Praise be to Allah, Who has spared me what He has afflicted you with, and has favored me over many of those whom He has created with a marked favoring," to be said upon seeing an animal with an injury, such as a limp?

It is not prescribed to say "Praise be to Allah who has spared me from what He has afflicted you with" when seeing sick animals, because Allah has favored human beings with intellect and speech over the rest of His creation, and no such practice has been reported from the Prophet (peace be upon him) or his companions. The noble hadith (definition) refers to physical or religious affliction that befalls a human being, not an animal. This remembrance is recommended when seeing a person afflicted with an illness or a deficiency in their body or their religion.