What are the practical difference between an RBM and autoencoder?

I've been working with stacked autoencoders for unsupervised training and using it for some (semi)supervised classification. As I read more, I wonder how I can justify using stacked autoencoders over stacked RBMs (a deep belief network). I know the fundamental differences between them (AE learns a representation of the inputs and is deterministic; RBMs learn the statistical distribution and is probablistic). But how do they differ in practical settings? When would you use one over the other? (or specifically for me, how can I justify using stacked AEs for classification over RBMs?) I'm trying to do my training and classification as unsupervised as possible (yet I need some labeled examples for the classifier).