Considering that the role of units (Specifically Line Infantry) of that time was essentially to form a line and shoot/be shot at by the enemy, how did these 'veteran' units work exactly? What made them less cannon-fodder than any other unit? I can see their veterancy coming in handy in terms of hand-to-hand combat and use of their rifles, but why exactly were they so renowned?
Also, did commanders ever make attempts to target specific veteran units during combat?
I can speak only of the French Old guard, I don't know very much about the Coldstream Guards but I can speak broadly of the purpose of Guard Units throughout European armies during this time period and more precisely on the Old Guard.
To join the Imperial Guard, a soldier must be younger than thirty-five years of age, have served Ten Years in the French Army, and had been a member of three major campaigns (such as Egypt, Italy, Austerlitz Campaign). There was a high requirement (of six French feet) but it wasn't as necessary because often this rule would be played with; Marshal Davout once told a prospective applicant to place packs of cards in his shoes to meet the height requirement.
From hear, the French Imperial Guard was always meant but rarely used to be a decisive unit who's near unbreakable morale would help decide the day. Famously this would be seen during the Battle of Marengo when Napoleon would commit the Consular Guard (forerunner of the Imperial Guard) to move forward and hold the line long enough for General Desaix's corp to arrive on the battlefield. They were nearly destroyed completely but their stubbornness helped keep the Austrians at bay long enough for Desaix to make a daring attack.
On the battlefield, a Guard division/corp/army would often be far in the rear and act as a reserve. They would be far enough behind the main line that it would be ineffective to fire upon the Guard and more importantly, artillery would have a more important job either working on counter battery fire or on the enemy line itself. Further, they would be so far back that they wouldn't be able to see which regiment is which.
What made the Old Guard so precious was how much was placed into the Guard. They would often have honors which I go into detail here.
Finally, most nations during this time period would have their Guard units either made of quality soldiers or made of nobility that would be use the guard rank to move into promotion quicker (privates in the French Imperial Guard would often be able to move out of the Guard and into the Line as Sergeants or better). However, these units would rarely be committed into battle since they're so valued.