In general you can pump more power through a pack and head system, they're also more versatile (lots of different setup options, you can mix and match). Monolights are lighter weight in total and more compact and so suitable for mobile shooting, they're cheaper and easier for beginners to use.
This is a generalisation however, each system has it's own pros and cons:
Pack and head
- + The heads are easier to position as they are lighter than monolights
- + Can use the heads with different power sources i.e. mains and battery
- + Single power pack for multiple heads (modularity)
- - Single point of failure (the power pack)
- - Wires everywhere!
- + You can control the power output centrally (instead of climbing up a ladder)
- - You tend to have less control in general (the older ones can't adjust the power to each head individually)
- + You only need one radio trigger / sync lead per pack
- + Simpler, lighter, more compact
- + Usually cheaper
- + Each light can be plugged into a wall socket locally
- - Limited to a single power source (mains)
- - Power output tends to be lower
- - Have to adjust power output on the head itself, which may be remote (unless you have a newer head with remote power control)
- - Likewise each head must be triggered individually (though optical slaves make this easier)
As you can see they are each useful in certain situations. A lot of people own / use both, for example the main lights might be powered of a single pack with a few monolight satellites which are further away.