Is a manufacturer certified pre-owned car better than a dealer certified one?

They are different products, so compare the written terms rather than the label. A manufacturer CPO program follows the automaker's inspection standard and its warranty is backed by the automaker, so any franchised dealer of that brand can usually do covered repairs. A dealer-certified program is set by that dealer or a third-party company, and coverage, deductibles and where you can get repairs vary widely. Ask for the inspection checklist and the warranty contract before you buy.