To be honest, I think that this question is too simple. There are certain things that Western culture would likely have been worse off without that the Romans produced, but others that would have made life better that they destroyed.
For example: The Romans revolutionized warfare. Along with this, they created a vast network of stable roads which connected all of the Mediterranean world, and made impressive architectural achievements with the perfection of the dome and arch.
On the other hand: Greeks in Alexandria were one step away from creating steam-power before the Romans burned down the library of Alexandria, which, by the way, was the vastest assembly of knowledge in the entire world at the time. Washing on a regular basis was made taboo by Roman society after they defeated the Gauls (who invented soap) which put Western culture behind on hygiene by, oh i don't know, two thousand years. Carthage was noted as having one of the most advanced infrastructures of any city in the world, with indoor plumbing throughout the city and multistoried apartments. Carthaginian knowledge of navigation and their mapping of the coasts of Africa were also lost.
And all this is ignoring the vast genocide caused by Roman conquests.
For this reason, it seems that the scale tips in favor of Rome being more detrimental than the barbarian hordes as far as knowledge and technology are concerned.
For example: The Romans revolutionized warfare. Along with this, they created a vast network of stable roads which connected all of the Mediterranean world, and made impressive architectural achievements with the perfection of the dome and arch.
On the other hand: Greeks in Alexandria were one step away from creating steam-power before the Romans burned down the library of Alexandria, which, by the way, was the vastest assembly of knowledge in the entire world at the time. Washing on a regular basis was made taboo by Roman society after they defeated the Gauls (who invented soap) which put Western culture behind on hygiene by, oh i don't know, two thousand years. Carthage was noted as having one of the most advanced infrastructures of any city in the world, with indoor plumbing throughout the city and multistoried apartments. Carthaginian knowledge of navigation and their mapping of the coasts of Africa were also lost.
And all this is ignoring the vast genocide caused by Roman conquests.
For this reason, it seems that the scale tips in favor of Rome being more detrimental than the barbarian hordes as far as knowledge and technology are concerned.