A brief glance at the ARM data sheet would suggest that the main difference between the TI mode and Motorola mode have to do with their handling of an output signal called SSPFSSOUT which many devices simply don't need. This signal is supposed to pulse high between bytes so as to indicate which bit of each byte should be considered the first. In TI mode, it goes high during the transmission of the last bit of a byte, while in Motorola mode it goes high and then low between bytes. The flash chip wants a chip-select signal which is held low for the entire duration of a transaction, so an output which goes high between bytes won't be useful for it.
I would expect that even when SSPFSSOUT isn't used, Motorola mode would make data easier to read on a scope (since there would be a pause after every byte) but TI mode might be faster (since it wouldn't waste any time pausing between bytes). What's important, however, is to ensure that the sequence of signals the controller generates meets the requirements given in the peripherals' data sheet.