(I apologize for any grammatical errors and for lacking sources. It's quite late for me)

I don't have a fully supported, factual answer to your question, however, I would like to give a few points regarding your question in general.

1: Context of Caesar's Civil War: Equipment Identification

While Roman armies are notorious for their drive to standardization within individual legions following the Marian reforms, it should be noted that this uniformity wasn't always reached (if it could be reached at all), especially considering the stratification between Caesar's and Pompey's forces, especially considering equipment (which would, in this case, be an identifying factor). For instance, Caesar had four veteran legions and some three levied legions, meaning that four would be equipped with the best Rome could offer (along with whatever looted or acquired equipment the veteran Legionaries used), while the levied legions would be equipped with what was available. Similarly, Pompey levied some eleven legions for the war, again equipped with whatever was available. While it would of been in the best interests of both leaders to equip their new levied legions with the "standard" equipment, that, given the situation, couldn't of been possible. For example, there was only a (give or take) year gap between Caesar crossing the Rubicon and the first significant battle, with Caesar and Pompey both running around their respective sides of the Adriatic seas. Given the time and the action restraints, I doubt standard loricas (squamata, hamata, etc) could of been procured for a total of some fifty-five thousand men. Thus, there was probably a clear difference in equipment. (and I wouldn't want to have only a shield and helmet for protection when I'm facing a legionary who's been gutting Gauls for eight years)

2: Banner and Heraldric identification (War of the Roses, US Civil War, Caesar's Civil War)

History's shown us that in Civil wars, each side will (deliberately) make means of identifying one another (for the most part). I've hastily brought up 3 examples.

a) The forces of Caesar and Pompey fought under distinctive banners and identifying factors. For example, each legion fought under it's own standard and various means could be used to identify friend from foe (or foe from friend in this case), such as insiginias or designs on shields.

b) Civil War: Rather straight forward, after the initial, early conflicts, each side (Union and Confederate states respectively) sought to identify one another by implementing different uniform colors (respectively).

c) War of the Roses: Similarly to point A, the Yorkish and Lancastrian forces both sought to identify each other by aligning themselves to either the Red Rose of Lancaster or the White Rose of York (of course lesser houses would then align themselves to either Rose with their own insignias and heraldry and such)

3. "Identical troops"

From my knowledge, I don't think there ever was armies of identical troops clashing together. Mainly due to the fact that military uniformity, especially on equipment, is hard to reach due to the stratification of social classes (Wealth and opportunity) and diversity of equipment choices (impediment to uniformity), especially in the context of the primarily feudal societies (of Western Europe) of the High and Late Middle Ages. For instance, Knights, Nobles, and Men-At-Arms (of England, let's say) may all be fighting in full plate, however, these suits wouldn't be identical or uniform (But they may conform to a style of armor). The same goes for the peasantry and gentry.