I don't think it has much to do with whether it was shot digitally (there are plenty of really grimy movies that were shot digitally, OT looking stuff could've been done easily and probably would've looked great), it's just all visual design problems with AOTC and ROTS.
Everything had to look hyper-slick for some reason. Wonder if it might've had something to do with Lucas overcompensating for losing the visual effects academy award to The Matrix?