I was reading an article about rotary engine and here is a part of it:
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"Wankel's engine does offer some advantages over the more popular piston powerplant. The rotary has a higher power-to-weight ratio and specific output, mainly because one effectively acts as three pistons. Case in point: the new RX-8 displaces 1.3 liters, but produces horsepower in a league with the 3.3-liter BMW 330I and 3.5-liter Nissan 350Z. Rotaries tend to be smooth runners as well because using two rotors offsets the primary up and down vibration. The rotary is far from perfect, though. Early engines had trouble with the rotor seals, emissions have always been a problem, and engine repairs quickly become costly.

Mazda continues to sing the virtues of the rotary long after Citoen, Mercedes, Ford, and GM (to name a few) have given up. The new Renesis benefits from these years of development and holds its own for power, efficiency, and emissions. With the RX-8, you can reap the rewards of Mazda's hard work."
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Hope, this will shed some light on "power doubts"...

There is no direct correlation between a rotaries displacement and a normal piston engine.

A 1.3 Liter rotary is a much different engine than a 1.3 liter piston.

However, the quote is correct about the power to weight benefit and that is what it is all about.

-Mr. Wigggles