The upgrade ("sticker" type) should nearly always be equal or more than the difference in fare on the original booking date. I can think of a few edge cases where this isn't true, but the vast majority of the time buying F outright should be cheaper - fare difference won't be less than the differential unless there is an unmatched K fare or a typo in either the fare table or the upgrade offers.

Note this only applies to differentially priced routes (most or maybe all First-marketed routes), and not to Polaris markets. The differentials used for the upsells to Polaris don't seem to have any direct relation to the fare table.