Since the beginning of Mixed Martial Arts competition, there have been two common set ups for combatants to compete in.
The "cage" set up is one of the most commonly recognized with leading promotions like the Ultimate Fighting Championship, Strikeforce, and Bellator being the leading promotions in American MMA where the cage is common whether it be an octagon, a hexagon, or rounded.
The opposing set up for MMA competitions is the "ring" which is borrowed from the leading combat sport of boxing, though the size of the ring may vary in different promotions. The "ring" set up in MMA is widely recognized from the classic days of PrideFC, and is commonly used in current day Japanese based promotions like Dream, Sengoku, DEEP, and also in European based promotions like M-1.
Comparing the two in a debate really comes down to many factors for die hard MMA fans. Which is safer for the competitors? Which provides the best opportunity for attenting fans to actually watch the bouts presented? Which makes the bouts more interesting? Which interferes less with a bout? And many more.
Which do you prefer?