For fixed rate loan, you don't need to worry the upside risk, ie hike in BR/BLR as the rate remains fixed throughout the loan tenure.  Fixed rate is not the spread of the bank (if it is under the context of "BR+spread" that you mean).  However, if the BR/BLR goes down, you will not enjoy the benefits of lower effective lending rate then.

Fixed rate loan is generally higher than the prevailing effective lending rate as the bank that offers the fixed rate loan needs to cover the possible rise in cost of funds in the future given that it cannot pass it through to the borrower.