The key concern is overloads. Both 15 and 20 amp breakers will trip on direct shorts (if they are working properly).
There is a tradeoff.
20A circuits have a convenience factor with the ability to delivery a considerable greater amount of power to a given situation. A typical example today would be a home office with multiple monitors, printers, computers and accessories in addition to whatever other routine loads (vacuum cleaners, electric heaters, etc.) are placed on the circuit.That extra 5A capability might just be the difference between adaquate wiring or a long-term headache of a constantly tripping circuit breaker.
On the other hand, the subloads on a 20A circuit might (possible) pose a safety issue. The 18 gauge lamp cord example has already been mentioned.
The danger being that if the 18 g. wire is overloaded just enough for the 18 g. wire to melt, but not enough to trip a 20A breaker. (In such a case, a 15A circuit breaker might be more likely to trip than a
20A breaker, but not necessarily). This is the reason that most power strips contain their own internal circuit breakers. 15A circuits were standardized during a time when there where few constant electrical loads and the loads were generally light. (a few lamps, a fan, etc.).These days, many people have home entertainment systems, hefty audio amplifiers, air conditioners, computers, big-screen plasma tv's, monitors, laser printers, and a whole lot of loads that could not be imagined 60, 70 or 80 years ago.
In my opinion, this makes the argument favor the 20A circuits over 15A circuits, just for the added capacity and convenience.
Beachcomber