I read a lot about this, from what I read some people seem to suggest that as an individual fighter the barbarian was much more capable being taller and stronger, but I think this is wrong. The Marian reforms required legions to be 5'10, and even without height requirements, from what I read the average barbarian was only 2-3 inches taller then a Roman soldier. As for strength, the Romans had a much better training regiment, it would ultimately depend on the individual for who's stronger, Roman or Barbarian. I think Romans were stronger due to their training and discipline, training with wooden swords and shield twice the weight of their standard weapons.
I know some barbarian units were just as armored as Roman Legion, in 1 on 1 combat a Legionnaire vs a Barbarian armored with chain mail and a Long sword, who would win? Would be logical to conclude that the Barbarian has an advantage with his Longer sword but does that make him stronger and a better fighter? No.
Also remember reading before the average Roman soldier was 5'6 while the average barbarian was 5'9.
If you look at the fall of the Western Roman Empire, when Barbarian units started to have a lot of Armour, it seems to me they won not because they were better or stronger but because they over-whelmed the Romans completely with numbers and the Western Roman Empire had a lot of internal struggles. Then later Belisarius comes along destroying the short lived OstroGoth kingdom, Romans in Africa continued to resist the Vandals. Then when the Eastern Roman control ended with a number of tribes moving into Italy, they were over-wealmed with numbers, I remember reading over 500,000 armed Barbarians moving in.