Advantages (or differences, that are advantages in some situations) that
apply to all pack systems:

-  More power  (this is item numbers 1, 2, 3, and 10 on the top ten reasons
list...)

-  You control the heads from the pack, so it is like having remotes for
every head that is attached - especially useful with a head in an
unreachable position on a boom arm, tucked behind furniture, or inside a
lightbank, say.  How helpful this is depends on how sophisticated the pack
is - independent assymetric power control is great, but costly;

-  A monolight is (almost always) in the form of a 'standard' flash head -
if you want to use ring-lights, striplights, boxlights, fish-fryers, etc.
you (almost always) need a pack system;

-  The same set of heads can be used with, say, a 6000Ws pack in the studio
and a 1500Ws pack when you want to go lightweight on location;

-  A pack head weighs less than a monolight, especially a high power one, so
with tall stands, booms, etc. you have less weight at the top, and can put
the heavy pack at the bottom;

-  Every head attached to the pack fires when you trigger the pack, so you
don't need to worry about whether slaves can 'see' each other;

-  If you have three monolights plus one that you use only seldom, you'll
have to remember to charge and fire it every now and again just to keep the
cap.s formed, whereas if you have a pack system the cap.s get exercised
every time you use any head with it;

-  The client thinks big packs look very impressive, and the assistant
develops huge biceps shifting them;    ;-)

Advantages that can apply, but don't within every system:

-  A pack plus, say, three heads is lighter than three monolights of the
same power (this isn't true as often as it should be);

-  A pack plus, say, three heads is cheaper than three monolights of the
same power  (this only tends to apply at the higher power end);

-  Potentially faster recycling;

-  Extra short flash duration tubes may be available for packs but not
monolights in some systems;

-  In the case of really sophisticated controls, you save by having the
electronics in only one place rather than duplicated;

-  Pack heads may be lighter and more robust than monolights;

-  Bitube and Quadtube heads necessitate a pack system.  With multiple power
packs you can use a bitube either plugged into two packs for more power and
shorter recycling, or plugged into one for shorter flash durations;

-  Some systems have accessories for things like sequential flash, interval
timing, etc. that only work with packs;

-  Some systems have full remote (sometimes wireless) control for packs, but
less often for monolights;

Possible disadvantages:

-  Packs can be  _very_  heavy, though some of the newest are surprisingly
light;

-  For anything up to, say, about three heads at about 500Ws or so each,
packs will probably cost a  _lot_  more than monolights;

-  If you have a pack and three heads, and the pack dies, you have nothing:
if you have three monolights and one dies, you still have two monolights...

Peter  (who uses both.)

<<I was wondering what the advantage in a
power pack strobe system is over that of the mono light system?>>

For portraiture...

1. Less weight aloft (e.g. hairlight), so lighter light stands can be used.
2. Lighter couterweights to balance the head on a boom, further lessening the
weight aloft.
3. Easier adjust light intensity and change lighting ratios, because you
control from the power pack, so you don't have to climb to adjust power.
4.  Fewer AC outlets to find (or fewer light strips to use)

Yes, White Lightning has ability to use optional control box connected to
monolights with phone cords, so Item 3 is not an advantage if you own the
control box, but then you have just increased the number of cords running to
the lights (fewer cords is one advantage that WL has advertised, and the
control unit negates that advantage).

For architectural work...

1. On the other hand, monolights have the advantage that each head ADDS more
light, not merely dividing the one available max power of a single power pack.

2. And you can light a wider area (e.g. large room easily without dropping the
power to the head because of long cables.  
3. And for architectural work, the AC cords can be hidden behind furniture
without the power cables that have to go back to a power pack.  

So you see that the choice of one vs. the other is highly dependent upon what
YOU need to shoot!

--Wilt

I think the rush to mono heads was started cause they are much cheaper for
the amount of light out put.

I think a small pack mounted on the side of a light stand makes a lot more
sense than a mono head attached way at the top of a thin metal rod.

the main advantage comes when you travel, especially for wedding photogs, or
home portrait shooters.  You can carry the entire thing in one hand nicely
balanced from a handle on the pack.  the head can stay mounted at the top,
the umbrella, I love to use a 40x50 westcott halo that opens like an
umbrella but you shoot through it like a softbox.  you can wrap the cable
around it to hold the halo and carry it from the car, set up in a minute,
rap it up in a minute.    Norman makes the only one I've seen designed to do
this, Photogenic makes a tiny power pack with enough power for 4 heads but
didn't put a clamp mount or hard point to do so.    The norman unit can be
powered off a battery too, but that's expensive.

I haven't been looking at what's available lately, but IIRC the small packs
are only 200 or 400 ws of power, adequate for old fashioned lighting set ups
like silver umbrellas up close, a bit under powered for large softboxes,
especially if you are shooting at f/16 like some do.  I prefer f/4 or 5.6 so
it doesn't matter much to me.  btw, by large softbox I think of large wall
to wall curtains of light, not a typical softbox of 30x40 or so.