We've talked about this elsewhere... but the Azera is closer to the Sonata than it is to the Genesis. It's a FWD midsize sedan.
Honestly, I think of the Azera as the Maxima of Hyundai (only better), the Sonata as the Altima (only better) and the Elantra as the Sentra (only there's no comparison, the Sentra is trash).
The Genesis and Equus are more like Nissan's
Infiniti brand, as Mr. B has said above. They're luxury RWD vehicles. I think there's plenty of room in the Hyundai lineup for all these cars.
The Azera may have been Hyundai's best kept secret in its current form, but I think it's gonna be their ace in the hole with the new model - I can definitely see it stealing a ton of Maxima/Camry/Avalon/Accord/TL sales in 2012!!!