With disciplinary actions, who typically comes down harder, COCs or IG?

Its all UCMJ, so its the same as far as punishment. The IG cannot actually give out punishment, a chain of command has to do that. UCMJ Authority lies with commanders. So the IG might do the investigation, but it will be a commander that does the punishment. Depending on the infractions, it may go right to a courts marshal instead of just an Article 15 level, but a Chain of Command somewhere has to initiate it. With the IG, it may be the installation commander that does that instead of a company or battalion commander that initiates it though.