Character Law has:
Races: common orcs, greater orcs, grey elves, half-elves, half-orcs, high elves, hillmen, mariners, nomads, urbanmen, woodmen.
Professions: warrior monk, layman, illusionist, animist, lay healer, healer, mystic, sorcerer, paladin, monk, magent.
Training packages: assassin, berserker, cloistered academic, con man, crafter, crusading academic, cut purse, detective, diplomat, explorer, guardian, highwayman, martial artist, mercenary, philosopher, sailor, shaman priest, spy, wanderer, weapon master, zealot.
It also adds some skills, including the martial arts skill categories and power manipulation skill category. Nothing critical here. Pretty sure these are all also in SOHK.
It adds talents and flaws. We don't use them, some styles of game may benefit from them.
Basically, I would say Character Law adds a lot of options for players making their characters. None of it is critical. If you have the sort of player who wants a ton of options, they will enjoy it. If you think the basics are sufficient, there's nothing necessary here.