Very little. All recipes, unless otherwise specified are read so that an egg is a large egg.
As you know, a "large" egg is a size, and size determines volume. The available volume in the shell limits the size of the yolks, and the chicken's genetic programming ensures that there be enough white in the shell with the yolks to support their development. So the proportion of yolk to white for eggs with twinned yolks is not hugely different than the proportion of yolk to white in normal eggs of the same size. In other words, each individual yolk in a pair of twins is smaller than the single yolk of a normal egg; while the total mass of the twin yolks is greater, but not hugely greater than the mass of the single.
A typical pound cake recipe calls for 1/2 dozen eggs per pound of butter. If you got one double-yolk egg in a carton of large eggs and used it in your pound cake, you'd be using 5 large egg yolks and the equivalent of 1 extra-large egg yolk, and 5 large egg whites and the equivalent of 1 medium egg white. Not a whole lot different from 6 large eggs. It's a rough equivalent to a difference of 1/2 oz in a pound. Not enough to make much of a change.
And, if you made the pound cake entirely from extra large eggs or medium eggs instead of large eggs it wouldn't make that huge a difference either. You'd still get a good cake.
Richer and denser, yes; but not by much. Not moister.
Even comparing slices from two pound cakes on the same plate, I doubt anyone could tell the difference. IMO, the "definitely affect" [sic] from pua.mella is wrong.