There are some clear advantages when using model-based recommenders. As mentioned already, scalability is one of the most important. Usually, the models are much smaller than the initial dataset, so that even for very large data samples, the models are small enough to allow efficient usage. Another benefit is the speed. The time required to query the model, as opposed to querying the whole dataset, is usually considerably smaller.
These advantages stem from the fact that the models are generally prepared offline, allowing for almost instantaneous recommendations. But since there's no such thing as free performance, this approach also comes with a few significant negatives—on one hand, it is less flexible, because building the models takes considerable time and resources, making the updates difficult and costly; on the other hand, because it does not use the whole dataset, the predictions can be less accurate.
As with everything, there's no silver bullet...