As to what the differences and common characteristics between the two company types are:
1) The tax rate is the same (approximately 21% up to 8 million JPY in taxable income),
2) They have the same legal protection (shareholders/partners are segregated from company’s liabilities),
3) GK is a separate entity from the holding company back in their own country. Therefore, there is no pass-through effect of its income/losses up to the holding company. Also, carried tax losses (if any) in Japan will stay in Japan.
4) On the contrary, a Japanese branch of the US company will be taxed in Japan first and then the Japanese tax the branch pays will be deducted from the corporate income tax of the main office back in their company (foreign tax credit). Also, the loss in Japan should be able to offset against income for the main office. The main office and the branch are the same legal entity at the end of the day.