What are the advantages and disadvantages of the two systems? Why isn't there one standard only?
well, these systems are different for historical reasons - something was decided on as a standard in one part of the world and something else, at the same time, in a different part of the world. it's just like driving on the right vs. left.. they're different, and incompatible, and it's a massive pain in the rectum.
but like driving, changing either system over to the other requires overcoming a massive amount of social inertia and a huge infrastructure cost - everyone would have to replace their appliances/cars, power-distribution systems/traffic signals would all have to be replaced. and because of the nature of these systems, you cannot "phase in" a change - it would all have to switch at the same time in one ugly go.
functionally there is no real difference in using 50 or 60 hz.
however, a different voltage has its advantages and disadvantages. 240V distribution is considerably less safe than 120V - get across 120V and you can be electrocuted for sure, but it's far far more dangerous to be electrocuted by 240V. so safety is one factor that favors a lower voltage.
on the other hand, for a fixed requirement of energy usage, a higher voltage will require a lower current. this is easy to see if you look at the equation for power in an electric circuit, P = VI. double the voltage and you halve the current.
they tell you not to plug a lot of energy-hungry appliances into a single outlet because doing so increases the amount of current that flows through your household wiring - too much can cause the wire to get hot and melt, possibly starting a fire and certainly causing costly damage. so a higher voltage power distribution system will be generally cheaper (less current = smaller wires = less material costs - this is part of the reason that long-distance transmission lines are stepped up to 120 kV) and less prone to failures from overloading. so that is an argument that lends itself to choosing a higher voltage.
so, both have their ups and downs - ultimately i think the choice is pretty arbitrary, but the different standards are going to cripple any movement towards a global society.