Each has it's advantages/disadvantages.
The biggest advantage I see in a closed system is what the available static pressure does for pumping problems. Starting out with a built in positive pressure present at the pump suction eliminates a host of issues with cavitation and suction boiling. Thousands of pumps are burned up every year because there is not enough pressure at the impellor inlet to prevent the hot water from turning to steam. This happens because the pressure drops below normal atmospheric levels allowing the water to literally boil at less than 212*, especially with under sized tube and over sized pumps used to compensate for it. Keeping the whole system in positive pressure territory "fixes" that problem.
The biggest disadvantage is also pressure and the effects it has on the cost of equipment built to handle it. Those of you who have large pressurized storage (mandatory IMHO) know how costly that is to buy and how time consuming it is if done yourself. A comparable unit that is unpressurized will always be less expensive to buy. There is also the rare but not insignificant matter of a boiler explosion which is not possible in a normal open system. When liquid water turns into water vapor quickly the results are nothing short of catastrophic. Judging from comments I have seen here in the past, I don't believe that too many people really grasp what a steam explosion can do to the structure it is located in.
As for open systems, the most common problem is the reverse of the first issue I spoke of in the first paragraph. No pressure or even negative pressure at the suction inlet of the pump. Usually this can be overcome by correct tube sizing that establishes a low head in the system and heating circuits but only those who take the time to educate themselves learn this the easy way rather than the hard way, buying pump after pump after pump for the life of the system.
As a general rule an open system will fail before a closed system not because of inferior quality or design but rather, a lack of maintenance. They do require monitoring water quality more closely than a closed system but to say a closed system needs no water quality maintenance is a false statement.
An open system is incapable of causing a catastrophic explosion or failure and is more inherently safe especially when is contains a large volume of water.
Open systems are nearly always less expensive to install up front and also less expensive to buy.
