From what I've read, aurors deal with issues related to the dark arts whereas hit wizards deal with the criminal types.
Lexicon says that aurors are trained for stuff like concealment, disguise, stealth, and tracking while hit wizards are trained for defensive charms, counter-curses, restraining lawbreakers without breaking statutes...so aurors are more FBI/CIA and hit wizards are more soldier/police? Petty crimes are handled by other ministry groups, when there isn't a high risk of being hexed or killed.
This could be an interesting subject to bring up in the L2 meeting...how maybe, since the rest of the ministry is in a shambles, and they're missing all their leadership, the aurors and hit wizards/witches have been forced to do menial tasks that are below their training while the bigger badder criminals get away with murder?
*will add more later, needs to nap*