Characteristics Auxiliary Regular Warband
Range 170 120 120
Arrow 9 7 7
Armor 3 0 3
Defense 4 2 2
Costs 430 190 270
For missile dueling, regular archers needs +2 arrow and +3 armor to come to par with the auxiliary. Shorter range for regulars is a problem for them but let's compare the costs without the range variable. That means to be at par with Auxiliary, the Regular archers need spend 2*20 + 3*30 = 130 denarii extra, or 130+190 = 320. The auxiliary is deficit of 430-320 = 90.
Having shorter range means the regular archers need to come up closer and spaced by 50 m with infantry or protective cav (or else the auxiliary will switch to shoot infantry). So auxiliary is more advantageous despite the 90 cost.
Auxiliary also has +2 more in hand-to-hand defense, thus could resist some cav charge better.
Back to the dueling aspect. In denari level that doesn't allow to fill up all the slots when use expensive units (8k or below), deploying many more archers may be quite advantageous. +2 in attack and +3 in defense may not compensate for twice the number of incoming arrows. If allowed to be ganged up, two regular archers only costs 2*190 = 380, while auxiliary archers costs 430.
Now, we could consider use of cav to counter auxiliary. Some cheap cav may just turn and run when came close to the enemy line. However, some cav just slightly more expensive than an auxiliary may be used to harass auxiliary. This is a factor to consider: enemy may sacrify a cav to disperse a couple aux. Bringing up a unit that could chase the harassing cav may actually get that unit shot.
Auxiliary archers maybe better, but not always.
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