/u/daVulpes pointed out some good, Occam's razor, universal advantages of veterans over recruits. However, when it came to Roman legionaries, the difference was even more profound than that.

The training of legionaries was quite dissimilar to the training of a modern soldier. There was no boot camp, no training courses, no graduation, no sudden point at which a soldier "qualified". Rather, Roman soldiers were trained constantly throughout their careers, and their skills and experience would accumulate over time to the point that veterans of several years constant campaigning would effortlessly defeat raw recruits. A prominent example of this is the Battle of Pharsalus as mentioned above.* An excellent example is the difference between the performance of a really elite army, like that of Scipio Africanus' army at Zama, and the really mixed performance of troops in Greece only decades later.

After the catastrophic Roman defeat at Arausio, Gaius Marius was put in charge of raising a new generation of Roman soldiers. Note the care he took in training them over long periods; in fact he sharpened his army for years before facing the Germans in battle (Plutarch Marius 13-16). Roman training took the form of daily weapons training, regular marching, and even more regular physical labour. The Roman conception was the physical labour, such as castramentation (the building of camps), was an essential element of discipline. Roman literature is dominated especially in the Imperial period (note esp. Corbulo, see Tacitus Annals books 13-14) by the need for Roman soldiers, who apparently had a tendency to lapse in their discipline if not constantly at work, to be constantly drilled with physical labours. It is these constant labours, as well as other fatigues and their combat training, that formed the much-celebrated Roman disciplina militaris. Training was a constant and prolonged process.

Let's use your Total War analogy, and lets use the example of Caesar's veterans. Veteran legionaries would have had higher weapon skill due to their much longer period of weapons training, as well as actual practice in battle. Their morale would have generally so superior to that of raw recruits that it is hard to overemphasise, a combination of their experience and the confidence that comes with their past victories would have made them far less prone to the panics that are typical of inexperienced soldiers. Their physical fitness would have been superior (unless they were old men, eg. Tacitus Annals 1.34) due to a much longer period of physical training, and the issue of physical exertion is also tied to morale: confident soldiers who have always been victorious will always have "more in the tank" so to speak than recruits.**

tl;dr: I doubt Total War could possibly exaggerate the superior stats of veteran legionaries, such as those of Caesar or Scipio Africanus, compared to raw recruits.

Note on sources:

My main primary sources as noted are Plutarch Marius, Caesar Gallic Wars

An important source on the issue of Roman training, and its nature as a constant process that was never really finished, is Phang, Sara E. Roman Military Service: Ideologies of Discipline in the Late Republic and Early Principate, New York, Cambridge University Press, 2008.

*Note that Pompey's troops were actually, many of them, veterans too. But it takes significant time for soldiers to get "fighting fit" and truly hardened for the sort of the battle Caesar's soldiers were recent veterans of, so even despite their experience Pompey's men weren't up to scratch.

**Examples include the endurance of Caesar's right-flank legions at the Sabis (Caesar Gallic Wars 2.25-27), and their readiness to fight again immediately after their repulse at Gergovia (7.51).

I don't have the percise sources, but Livy wrote a fair share about the Legions in his 'History of Rome'. Ceasars' 'De Bello Gallico' would be another source. For the Civil Wars Cicero and Plutarch would be potent sources.

Basically it boils down to what you already mentioned - battle experiance.

A seasoned veteran would be used to the phyiscal strains of battle. He would be used to the noise and the smell. The screams of the wounded and the foul stench of the dead. These were (and still are) the main psychological stress-factors for soldies. A raw recruit might have been well trained (physically) but there was (and still is) very little training that can prepare you for witnessing death in a close combat situation.

On the other hand are veteran units used to actual fighting. Once close combat started the neatly trained tactics and techniques were faced with the chaotic situation of the battle. A vertran unit would be used to this chaos and would be a lot better at handeling this chaos. Meaning: staying in close formation, not opening up small gaps for the opponent to attack, ... Since centurions did fight alongside their men and so it was not all that uncommon that they were incapacitated or even killed. A veteran-unit would have been able to compensate the loss of their officer a lot better (due to experiance with such situations in previous battles) that a freshly levied unit.

And lastly, since we are talking about the civil war, it should be mentioned that Ceasars' Legions (as well as all other pre-existing ones) had years of training while many a Legion was levied in a hury during the civil war. So not only were those raw recuits but their training was also short and thus inferior to those Legions who were raised by Ceasar for his campaign in Gaul.