Having specialized cells means your cells have the potential to become much more complex. They can lead to having complex tissues/organs/organ systems and the categorization of tasks because you're compartmentalizing and dividing the work up within the organism. This means that while some cells can take care of survival tasks, other cells can allow for growth and development of the organism as a whole. In organisms with even more specialized cells, this is seen more! The more specialized the cells, the more complex the organism, and the more the potential for development. You can see this in eukaryotes vs. bacteria, animals vs. plants, even mammals vs. reptiles. Monkeys are much more complex than lizards. Most people would agree that humans are the most complex (they're not "better" they just have more specialized cells).
Disadvantages:
A lot of energy is invested in specialization of cells.
Bacteria, Archer, some protests, etc, don't have specialized cells so they can devote a lot more energy to survival and reproduction. For example bacteria are really, really abundant. They have the highest population out of all the organisms in the world.
