I think the main difference was preparedness. Vivio clearly developed countermeasures to each of Nanoha's specific moves, spent most of her childhood practicing against her moma's homing bullets and has experience getting hit by what was probably Nanoha's biggest starlight breaker ever. Nanoha on the other hand, while generally taking the fight seriously didn't have as many specific strategies for dealing with Vivio and mostly just went with the standard tactics for fighting someone with Vivio's style. More than anything, the anti gravity environment the match took place in was what allowed Vivio even the slightest chance of winning, as in normal gravity she wouldn't be able to get near Nanoha fast enough once she took to the air and Nanoha would blast her to smithereens. In the end, while Nanoha didn't get up from the down, she still had magic reserves and probably could have gotten up and continued fighting in a real combat situation, whereas Vivio was at that point completely out of magic and definitely wouldn't be able to continue fighting despite standing up. Only in the context of a match like this would this be considered Vivio's win. Also the tricks Vivio pulled wouldn't work a second time and Nanoha would easily win a rematch.
So yes, Vivio can win against Nanoha in a one on one duel, but only under specific rules, in very specific environmental conditions, while Nanoha is underestimating her and with a fair amount of luck.
Like they said back in the StrikerS manga chapter 10, there's no such thing as the strongest because in reality whether you win or not is determined by how well the combat situation is suited to your particular skill set.