nologic - the answer to the question of why purchase I over EE is one that's somewhat difficult to answer. I bonds are inflation protected bonds, whereas EE are standard bonds which pay a rate of interest linked to current market rates.
Having said that, one reason to purchase I bonds is that the annual purchase limit per person (imposed by the US govt - not by AMEX, as your post suggests) is 30K. EE bonds, which are purchased at the discounted face value have an annual purchase limit of 15K per person.

So, if you only want to buy one series of bonds, you can purchase more I bonds than EE, but that's relatively inconsequential. In addition, you can purchase both series if you wish.
And, yes you can use MC/Visa as well....again, this is something determined by the govt. Best wishes.