Obviously you will get different output because in first case you are creating SUM of individual symbol MFIs while in second case you are creating single MFI from SUM of prices. Sum of prices can be considered "index". So in second case you are calculating MFI indicator of the INDEX.
MFI indicator is not addition. It does not have properties of addition. MFI is notcommutative with regards to addition. In other words the ordering of MFI and sum matters.