What value does it really give? What do I get out of it?

What's so special if I have a high specific output for my engine?

Why did Honda brag about the 100 hp/li B16A engine when it first came out?

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High horsepower rating = engine is more powerful on top-end, has faster top-end speed

High torque rating = engine is more responsive

High specific output rating = ??????

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Take this case between a 1.3 and 1.6 engine where the 1.3 gets more specific output:

Mazda B3 (Gen 2.5)
73 hp / 1.3 liters = 56.15 horsepower per liter

Mazda B6 (Astina)
88 hp / 1.6 liters = 55 horsepower per liter

Does that mean I can almost "feel the same power" when I downgrade to the 1300 engine?