Live attenuated viruses can serve as an effective way to immunize individuals. These vaccines are weakened forms of the “naturally occurring” vaccines. These vaccines are able to replicate within in the individual. Because of this, the immune response is more similar to a natural immune response and effective immunization usually requires only one dose. Although it serves as an effective way to provide immunization, it also comes with some negatives. These immunizations are more likely to cause severe reactions. Furthermore, since they are in fact live vaccines, they shouldn’t be used to immunize those who are immune compromised. Proper care should also be taken to store these types of immunizations.

Inactivated vaccines are either composed of the whole organism or parts of the organism. These vaccines are not capable of replicating and therefore typically don’t elicit the same magnitude of immune response as live attenuated vaccines do. These typically require 2-4 booster vaccines and their immune response is mostly just humoral and does diminish over time. It is worth noting, however, that these types of vaccines can be given to those who are immune compromised, since the vaccine isn’t capable of replicating within the individual.

In terms of the actual differences in immune response elicited by these two techniques, they both elicit a similar titer of serum IgM, IgA, and IgG. However, the live vaccine is the only one of the two that also elicits a Nasal and Duodenal IgA titer.

As you can see, both of these techniques have different pros and cons and their use is entirely situational depending on an individuals need. Depending on the circumstances, both can serve as an effective way to immunize an individual. 

Source. 

1. Immunization Basics Power Point