As I'm listening through Andrew Roberts' Napoleon: A Life, I continue to see a recurring theme where capturing Imperial Eagles becomes a measure of defeat for Napoleon especially past 1812. For example,
Krasnoi in 1812:
The Russians claimed 13,000 killed, 26,500 captured, 133 guns and fifteen colours, standards and eagles taken, as well as Marshal Davout's baton
Leipzig in 1813:
The Allies captured 15,000 able-bodied Frenchmen, 21,000 wounded or sick, 325 guns,[4] 28 eagles, standards, or colours, and most of the French supply trains. Six French generals were killed, 12 wounded, and 36 captured including Lauriston and Reynier[4]
Waterloo in 1815:
The Greys captured the eagle of the 45th Ligne and overwhelmed Grenier's brigade. These would be the only two French eagles captured by the British during the battle.
Likewise from what I gleaned Napoleon remained tight-lipped on these losses while underreporting troop casualties. Were these Imperial Eagles prized by opposing forces for their rarity, monetary value, or as a psychological tool of conquest against Napoleon? If a psychological tool, do we have any evidence of leadership directing forces to concentrate on seizing these eagles above all else?
Here's the thing: for all that the eagles are new and unique to Napoleon, in all actuality they're really just a particular incarnation of something all European armies of the time already possessed - that would be the standards and colours also mentioned during Krasnoi and Leipzig. Put it another way, the eagles are colours in the same way that Champagne is sparkling wine. That is, they count as the larger category in all respects, they just happen to be unique to a particular region.
Thus, everything that applies to colours of all other nations also applies to French eagles, and thus I refer you to this previous thread ably answered by u/DonaldFDraper, with me assisting. Should you have any follow-ups, please don't hesitate to ask them!