Is it permissible to take out a loan from banks (traditional or Islamic) to purchase a house in installments, especially if the Islamic bank's rate is higher and non-decreasing?

Borrowing with interest is forbidden in Islamic law unless there is a necessity. Since purchasing a house is possible through Sharia (definition)-compliant Murabaha, there is no necessity here. The fact that the profits of an Islamic bank are higher than the interest of a conventional bank does not make permissible interest-based borrowing. Usury is the opposite of trade, and Allah has permitted trade and forbidden usury.