Absolutely gold coins will be deeper! The sink rate of a coin is based on two factors- It's weight and it's size. More size, more resistance to sinking. More weight, more ability to sink based on it's size. So a gold coin of similar size to a silver coin will sink faster. Coins sink until they reach a point where the density of the soil equals the density of the coin in terms of size and weight. That's why you'll find silver coins right on the surface in hard packed clay (I have in the woods at hard clay locations), where as ten feet away in better soil a silver coin of the same age could be 6 to even 12" or more deep. The moisture content of the soil also comes into play. I know of one site where the soil isn't ideal in terms of the best of the best in being "fine" soil, but it's one of my deepest old coin spots to hunt. In fact, at this very spot I dug a V nickle and an Indian in two separate holes at 11" with the GT and stock coil. The soil on that day was perfect in terms of being set enough to enhance signals well. This spot, though it stays dry most of the year, is a low field from a sloping hill, and so during the winter and spring months this field gets really soggy and wet...So, despite the soil not being the best, I believe that's the reason the coins are getting so deep there.
Even if you are finding silver coins at a certain max depth at that site, don't expect the gold coins to also be at that depth since they are heavier for the same sized coin. They'll sink deeper until they reach equal density with the soil, or at least sink faster than the silver of the same age has. For those two reasons that could cause the gold to be deeper, the only way I'd expect a gold coin to be found at the same depth as a silver coin that was dropped around the same time would be if there is say a layer or hard packed clay, stones, or bedrock at a certain depth that the coins seem to stop at. Once a site we hunted had about 12" of fine black topsoil stripped from it. Below this 12" they removed was very hard packed limestone clay. We found coins laying right on the surface of this layer. Several, in fact, and as suspected didn't really find any coins much deeper than the surface in that clay. That's despite all the silver that was pulled from the removed topsoil on prior hunts.