Actually birds are ZZ (Male) and ZW (Female). But for simplicities sake we usually refer to them in the mammalian terms XX and XY.
As with any species, budgies have dominant and recessive genes (or mutations as they are referred to when speaking about genetic alterations that in single or double form produce a phenotypical change). They also have mutations that are carried solely on the sex chromosomes, specifically the X chromosome as the Y chromosome seems either non-functional or perhaps non-functional in the sense of carrying phenotypically altering genetic mutations.
Some basic (but not exhaustive) examples of sex linked genes in budgies includes the common ones such as opaline, cinnamon and ino (both lutino and albino are the same gene acting on a white based bird <albino> or a yellow based bird <lutino>).
Because the sex linked gene is carried on the X chromosome, it is more common to see sex linked mutations in female budgies because of the fact they only have (and therefore need) one X chromosome in order to display that particular mutation whereas males would require the mutated X chromosome from both the father AND the mother in order to physically display the mutation (as opposed to being merely a carrier of it, which is termed 'being split for' a certain mutation).
Hope that goes some way toward helping...
Edit: Yes humans are the opposite - males are XY and females are XX