Upvote:2
The difference between Chasseurs à Cheval and Hussars is that, while both were light cavalry, Chasseurs were ALSO expected to act as dismounted infantry if the situation called for it and were trained accordingly. This in turn effected the types of missions they were assigned to. Hussars got a lot of what a wargamer/armchair historian would consider "traditional" light cavalry roles on the battlefield (scouting, harassment, etc) whereas the Chasseurs were often assigned to convoy protection, guarding lines of communication and so forth, though they could and did perform traditional battlefield light cavalry roles if required.
Generally speaking the Hussar regiments were considered more prestigious because they are "true" cavalry, whereas the Chasseurs à Cheval were supposed to fight dismounted, and indeed many were former dragoon regiments "converted" to Chasseurs à Cheval. In the ranks of "prestige" pure cavalry tended to view dragoons as basically infantry and therefor inferior, but there were some famous Chasseurs à Cheval regiments that probably "outweighed" the less prestigious Hussar regiments, depending on who you asked at the time!
Most of this information can be found on the wikipedia pages for Hussars and Chasseurs, with any gaps filled by my own knowledge of Napoleonic cavalry formations.