This web page
http://www.christianism.com/articles/article12.html
cites book From Sumer to Rome, The Military Capabilities of Ancient Armies, Richard A. Gabriel and Karen S. Metz
'The ancient world produced the prototype of every major offensive and defensive weapons system used by armies until the invention of gunpowder, and even then some armies of the ancient world would have made short work of the armies of the seventeenth and eighteenth centuries. The weapons of the past were simply of greater range, firepower, and lethality than those used by armies up to the Civil War. So proficient were the military establishments of the ancient world that war on a "modern" scale was already a fact of life long before the modern period began.' [xv].
To me, it seems incredible, is there any truth in such extraordinary claim?
There isn't very much evidence to support such a claim.
Keep in mind that militaries have evolved from past militaries, and as technology has evolved, militaries have replaced old weapons with new weapons that have proven more effective in warfare. Thus the English moved to gunpowder even if the Longbow had been a mainstay and proven weapon.
And that brings me to my next point: while individual weapons and systems in the past may have been of greater range, firepower, or lethality, war is more than just about having a very effective weapon.
Warfare brings about not just those weapons, but how those weapons are used, the quantity of said weapons, and a whole host of other factors that involves winning wars (the strategic side of things) vice individual matches (tactical side).
Take for instance the longbow. The English were known to train to use the longbow from an early age - to become a great archer, this would take years to develop.
With the advent of gunpowder weapons, however, this changed dramatically. Armies could now be raised and trained in how to fire said weapons, and learn close-order drill, and be fielded in weeks and months instead of taking years to grow and train an archer. And they could do that en masse which led armies to grow drastically in size: by the 17th and 18th centuries, armies - professional ones, at that - could number in the hundreds of thousands, whereas medieval armies and earlier were generally in the tens of thousands or even smaller.
So sure, a longbow on paper might have longer range, accuracy, and even lethality than a 1600's musket, but those musket-based armies were larger in size and could bring about more firepower overall and win wars.
The same could be said about ancient machines of war too - a ballista of the Roman era might fire a bolt very accurately and at long range whereas early cannons were rudimentary, inaccurate, and so on. But cannons would eventually be relatively easy to operate and load, were less influenced by weather, and could be concentrated (especially once they started being mass produced) to produce a far more effective overall war machine.
Technology is no different today and is even more lopsided. For instance, one could look at a battleship's 16 inch cannons and say "look, they have longer range and far more devastating firepower than the puny 5 in guns on a destroyer" - and that would be correct.
However, that destroyer's radar systems and missile systems could engage a fleet of battleships from hundreds of miles away and sink an entire force of WW2-era battleships with impunity. Indeed, the gap between the military today and the WW2-era militaries at the peak of their powers may as well be fighting militaries of two centuries ago.