Where possible I will use AMEX for all my personal transactions mainly as I have a longer interest free period on spends making budgeting easier, also while its a pure perception thing the few times I have had the need for a chargeback or had a problem with my card its been resolved in minutes.

Of course as a merchant it's higher fees, has weird conditions attached to it and virtually all AMEX users have another credit card (indeed Amex provide me with a visa card for when I can't use my amex) so there is little benefit to supporting amex.