The FAA examiners will look for depth of knowledge. That means they'll ask you about something and keep asking until they find what you don't know. You don't have to answer everythng correctly, just have the depth of knowledge required for your level of pilotage.
That said, ground instruction is REQUIRED! Video based instruction can be helpful, but not alone. Schools which only pay their instructors for flight time should be avoided, as you won't get the quality of instruction you need!
If you pick your school well, the US will be significantly cheaper. But there are a lot more schools to choose from.