How were meat dinosaurs and plant eating dinosaurs different?

Yes, just like there are more plant eating animals than meat eating animals in the modern animal kingdom.

The reason for this is that a species needs to maintain its numbers above a certain critical point. Below this point there aren't enough mates to make off-springs and extinction becomes imminent.

There is a general cycle which controls the number of carnivores:prey ratio, and it's a bit like this:

If hunters (carnivores) eat too many prey, then, there is a shortage of prey for the rest of the hunters. The hunters don't have enough food and therefore start to die out. When this happens the population of prey is no longer in danger and so increases. When there is an abundance of prey, the number of hunters increase once again and the cycle repeats itself.