For one, I definitely wouldn't attribute Roman success to the gladius. More to the shovel; their real strength was in constructing and overcoming fortifications, bridging rivers, and building roads to support forces far afield. A stout one handed spear would service them just fine if they had their shovels.

With the transition from the Roman Empire to its succeeding polities, heavy infantry ceased to dominate the battlefield; mounted men-at-arms became the most prominent weapon during the Middle Ages, and the Roman gladius was useless on horseback. When heavy infantry passed back into fashion during the Hundred Years War, full plate armor made shields, and thus shield walls, redundant, so knights had two hands for weapons. Fighting another man in plate armor, most knights would half-sword; that is, grab their sword by the blade for better control when thrusting or grappling, or turn it around altogether and batter their enemy about the head with the pommel and crossguard; another technique impossible with the gladius.

A very simple answer:

Roman cavalry never used the gladius. A short blade is useful on foot, but not on horseback since you won't be able to reach an opponent standing on the ground. Roman cavalry used the much longer spatha.

Knights were cavalry. So of course they used longer blades.

Another answer is metallurgy. Late medieval longswords were much superior to the Gallic blades. Polybius mentions that the Gauls often had to stop mid-battle to straighten their iron swords, which would bend under the impact of blows. A medieval blade does not do this. (And it's not heavy either. Heavier than a gladius, sure, but still under 2 kilos for a hand-and-a-half blade.)

Oh, and don't be so quick to dismiss "untamed barbarians." Guess whom the Romans copied their favourite sword from? There's a reason it's called the "Spanish sword." Most of those "barbarians" the Romans fought were a big threat, sword or no sword.

Still, that doesn't answer your question completely, since even the Roman infantry switched to using the long spatha in their later years. Why? I do not know. Something must have changed. But whether it's a matter of culture, technology, fighting style, different enemies, shifting status of the infantry, or something else altogether, I do not know.

It's a matter of much debate, and little conclusive evidence. It's discussed in this thread but I don't actually agree with the top-level comment, which refers rather out-dated stereotypes about Germanisation of the legions and some presumed loose-order fighting style on their part.

In the end though, the question may be less important than you think. In pre-modern times, the idea of an "arms race" and armies being stronger or weaker because of the weapons and weapons systems they use is rather anachronistic. Ultimately, a pointy stick is a pointy stick, even if one is a fancy ultra-stabby pointy stick. Neither will give a decisive advantage compared to factors like morale, generalship, numbers, training and discipline, or plain old luck. The Romans won most of their battles throughout their history and remained formidable long after their empire passed its zenith. They also lost at least one battle against virtually every enemy they ever faced. Polybius stressed the mechanical aspect of warfare a lot when he praises the gladius over the Gallic longsword or the Macedonian sarissa. The Romans themselves were more inclined to credit the courage and discipline of their soldiers and the favour of the gods. Modern military historians like Philip Sabin are actually inclined to think the Romans had the right of it, at least where the quality of the men rather than that of the equipment is concerned.

And when it comes to who wins wars, rather than battles? Even those factors will likely pale compared to the larger questions of logistics, manpower, diplomacy, and political determination and the will to fight.

It's somewhat debatable whether the gladius was actually superior to longer swords. A lot of it seems to go back to Polybius, who frequently brings up the fact that the Roman swords were apparently much better at thrusting than those of the Gauls. For instance this description of a battle against Gauls in 223 BC:

When the Celts had rendered their swords useless by the first blows delivered on the spears, the Romans closed with them, and rendered them quite helpless, by preventing them from raising their hands to strike with their swords, which is their peculiar and only stroke, because their blade has no point. The Romans, on the contrary, having excellent points to their swords, used them not to cut but to thrust: and by thus repeatedly hitting the breasts and faces of the enemy, they eventually killed the greater number of them.

However, he never actually gives the impression that the gladius was only made for thrusting. As he describes it, "It has an excellent point, and can deal a formidable blow with either edge, because its blade is stout and unbending." And in many instances he claims that the Romans were trained to fight with a 3 foot gap between each soldier so that they had room to swing their swords.

On the other hand though, the sword Polybius was describing was most likely the Gladius Hispaniensis, the type most commonly used during the Republican period, which wasn't particularly short. It was generally more than 30 inches long with a 24-26 inch blade. In the 1st century BC the Roman army largely switched over to the more famous Pompeii-type gladius, which was only 24 inches long with an 18 inch blade. The Pompeii Gladius was used up until the late 2nd century AD when it started being replaced by the much longer Spatha.