Does it matter whether my family case is in the Ontario Court of Justice or Superior Court for costs and procedure?

The basic Family Law Rules governing conferences, motions, disclosure, and costs apply broadly across both the Ontario Court of Justice and the Superior Court of Justice where they're hearing family matters, so the general procedural framework, and the court's discretion to award costs based on conduct and settlement behaviour, is largely consistent between the two. The more significant practical difference is jurisdiction rather than procedure: the Ontario Court of Justice cannot grant a divorce, deal with property division, or handle the matrimonial home, while the Superior Court of Justice can handle all family law matters, including those the Ontario Court of Justice cannot.

Because of this, which court you're in often depends on what your case actually involves, rather than a choice about procedure or costs — a case involving only parenting or child support between unmarried parents might proceed in either court depending on the location, while a case involving divorce or property must be in the Superior Court of Justice. Where a location has a unified Family Court branch of the Superior Court, all family matters are heard together in one place, avoiding this split; where it doesn't, cases can end up divided between the two courts. Confirm with a lawyer which court has jurisdiction over your specific issues before starting a case.