Raw stats don't determine everything in battle. Since the basis of the entire battle system is speed, you have to take attack animations into account. These attack animations have a huge impact on how quickly actions are implemented in combat.
Serah is generally faster than Noel is most aspects. This compliments her generally higher Magic ability and her suitability for Magic roles.
Animation speeds can vary significantly between monsters. For example, Chocobos are pretty fast while the more Western species are slower in comparison, despite their impressive stats. Another thing to realize is that Serah, Noel, and every species of monster have different physical attack animations. This is more than just an appealing-to-the-eye feature.
Noel's physical attacks have the distinct feat of landing two consecutive hits instead of one, with the properties of a single attack split in two. This split applies to the amount of damage inflicted as well as the effect on the Chain Gauge. It's not significant, but two hits are better than one, especially when it comes to maintaining the Chain Gauge.
Serah's weapon can take on the appearance of a bow or a sword. You can actually control which one she uses by tuning your Paradigms appropriately. In a Normal tune Paradigm, Serah will seem randomly switch between the two. In a Cross formation, she'll stick to the sword. In Wide fromation, she will stick to the bow.
Also, Serah's physical actions with the sword have a much faster animation speed than those with the bow. This doesn't apply when she is casting spells, so if Serah is your main spell caster, this information may not have much impact on your playing style. However, this is another reason to pay attention to the tuning of your Paradigms. For example, against a single magic-resistant enemy, Cerberus-X will likely quicken Serah's damage output as a Commando opposed to the regular Cerberus.
Another thing on physical attacks is that Serah and Noel both have kind of special 'finishers' that occur after they execute a full command queue of abilities once they reach an ATB Level of 4 or higher. These finishers tend to deal slightly more damage but are slower.
It's always faster to string together a sequence of the same actions rather than combining multiple different actions. In other words, switching between physical and magic in a command queue takes a lot more time than sticking to all physical or all magical abilities in a single command queue.
Serah and Noel also have different animations when airborne. Casting animations become much slower when they are in the air. However, this isn't necessarily a bad thing. Normally, the lack of speed will extend the time that an enemy will remain Launched.
Speed is also more important in some roles than in others.
Medics and Ravagers benefit the most from quick animations. For Medics, faster animations mean they will be able to heal their targets faster. For Ravagers, since their main purpose is to fill the Chain Gauge, the faster they can attack, the faster the Chain Gauge will fill, and the faster the enemy will be Staggered.
Speed for a Commando is also important. They faster they are, the more damage they can do in a shorter amount of time.
Part of a Synergist's efficiency depends on how quickly they can apply Buffs. This is especially important in a race against time when an enemy is about perform an especially strong attack.
While it's good for Saboteurs to inflict Debuffs in a timely matter, their efficiency is based more on persistence rather than speed.
For Sentinels, animation speeds don't matter. Their main purpose is to distract the enemy and take damage for the rest of they party. Even the slower monsters can fulfill this role sufficiently.