2 possibilita`:

- confronto tra stringhe:
var dat1 = "aaaa/mm/gg";
var dat2 = "aaaa/mm/gg";
if(dat1 > dat2) { ...

- confronto tra oggetti Date()
var dat1 = new Date(aaaa, mm-1, gg);
var dat2 = new Date(aaaa, mm-1, gg);
if(dat1 > dat2) { ....