Eggs contain proteins that have a fair bit of sulfur. It is Hydrogen Sulfide (H2S) that forms black silver sulfide which is the tarnish. When the eggs are cooked, the sulfur which is trapped in proteins comes out as hydrogen sulphide or other more volatile compounds that can react with the silver. Certainly boiled eggs always smell of some H2S. In the hard boiled egg, the temperature never goes above 100C, the temperature of boiling water. Also, the sulfur compounds are mostly kept inside the shell and cannot escape. In the fried egg, the temperatures can get somewhat hotter, especially as the water in the egg is driven off. In addition, sulfur compounds which are quite volatile can evaporate into the air. In this way, the boiled egg has more tarnishing power than the fried egg, because 1. temperatures have not been as high and 2. tarnishing chemicals have been kept in the shell.