Officers were indeed expected (but not necessarily required) to privately purchase their own equipment, including the cuirass, helmet and sword, but troopers were always issued equipment (often with marked differences in quality and in manufacturing, with troopers swords often being heavier and balancing further into the blade than officers swords. Seargents swords are usually somewhere in between the two, as they were also private purchase but necessarily cheaper). The total price for a full uniform and all equipment for an officer could be as high as 2000 francs, so many regiments needed to advance their officers enough money to get outfitted. This sometimes came directly from the war office funding and sometimes from regimental coffers. Troopers were always given a full uniform and equipment

Officers could use an issued cuirass (but still needed to purchase everything else). Many chose to purchase privately made or privately sold cuirasses because they wanted to have something that would distinguish them from both their troopers, and often other officers.

The armor was definitely issued, arsenalled, and sometimes reissued. One sure way to tell is that troopers armor will have arsenal or regimental markings, and officers armor will not. Some will have their original markings struck out and new markings placed below them if it was re-issued to another regiment.

Regarding more significant differences between officers and troopers: officers had a lot more leeway with privately purchased equipment. Many wouild have cast or repousse brass plaques riveted onto the front of their armor, depicting things like the imperial eagle or their regimental symbol. Some would be gilt, or even brass plated, however this was also true for some troopers armor - which can be identified by a combination of decorative elements, and a regimental marking. These were generally found on troopers from specific regiments, such as carabiniers who had brass plated (or solid brass) cuirasses regardless of rank.

Further detail, adapted from "Napoleon's Heavy Cavalry, the Cuirassier and Carabinier: Their Arms, Armor, and Tactics" Ricky E. Parrish

There were three different patterns of cuirass produced during the Napoleonic period. There were thirty-four copper rivets on the outside edge of the front and back pieces.

The "MkI" cuirass had a fairly blocky breastplate that formed a blunt angle at the bottom. This was made into a more rounded unit with the MkII cuirass, issued in 1806, and further rounded on the bottom of the breastplate with the MkIII cuirass, issued in 1809. There were belts at each shoulder and one at the waist that held the two pieces together. The shoulder belts were usually covered with brass scales; the exceptions were in the 8th Cuirassier regiment, which had bare black leather straps, and the 9th Cuirassier regiment, which user1 dual yellow-copper chains on their shoulder straps.

The officer cuirass more ornate, with gilded scales and silver lace down the length of each piece. One difference in the three patterns was that the officer's MkI cuirass only had thirty-two copper rivets, whereas the MkII and MkIII patterns called for thirty-four gilded rivets

The Carabinier cuirass was the same basic piece of armor as the mkII cuirass, except for the thin sheet of brass that covered the iron, leaving only a 25mm border around each piece, where the yellow copper rivets were placed. The straps on the armor were of natural leather with copper fittings. The officer's cuirass was very ornate, with a red copper sheet instead of brass; there was also a silver sunburst placed on the center of the breastplate. The Carabiniers did not receive their armor until 1810

Regarding helmets - standarisation was basically non-existent, but troopers often had yellow copper alloy / brass helmets, and officers often had red copper alloys.