I don't know if you still need an answer but anyway I hope you will find this useful.
A CDBN adds the complexity of a DBN, but if you already have some background it's not that much.
If you are worried about computational complexity instead, it really depends on how you use the DBN part. The role of DBN usually is to initialize the weights of the network for faster convergence. In this scenario, the DBN appears only during pre-training.
You can also use the whole DBN like a discriminative network (keeping the generative power) but the weight initialization provided by it is enough for discriminative tasks. So during an hypothetical real-time utilization, the two system are equal performance-wise.
Also the weight-initialization provided by the first model anyway really helps for difficult task like object recognition (even a good Convolutional Neural network alone doesn't reach good success rate, at least compared to a human) so it's generally a good choice.