Both are valid methods for measuring rain rate. A better question is which is more useful. If you're in the middle of a storm, you'd care more about how hard it is raining at that particular moment, is it pouring out there, or has it let up to a drizzle. In this case, the (nearly) instantaneous rate is more important since it tells you how hard it is raining at that moment.
On the other hand, after a storm has passed, how much it rained at any one moment is less important. Now the amount of rain per hour is more important.... however, with such a long time frame for measuring, the usefulness of "how much rain did it rain per hour" more closely resembles the total rainfall.
Taking galfert's car analogy, which is more important to someone watching you drive, how fast you're going at that moment, or a summation of the total miles/kilometers you've driven in the past hour. "I'm sorry officer, I know your radar says I was going 60mph in a 45mph zone, but I've only been driving for 10 minutes so really I've only gone 10mph so far this hour".