Since you are referring to Sweden i might chip in as well. Amex acceptance rate in Sweden is pretty much constant. Most (all) larger restaurants/bars, shops and stores does accept Amex. Even McDonalds does
There are a few notable exceptions, for example IKEA stores. Smaller establishments have rarely accepted Amex/Diners even in the past. I am not sure that the chip is a big factor, it's more likely the higher fees. Even swedish-issued Amex cards does not have the chip, but i heard it is supposed to be introduced during 2010. Even without the chip, Amex cards does come with a PIN so i usually doesnt have to sign the slip, i can sign by using PIN in the terminal.
It is a fact that swedish banks (which all issue chip/pin cards now) is leaning heavily on the merchants to go towards chip-enabled terminals. This is the new small grey boxes you probably have seen in the stores lately. These conform to the new EMV standard which will be mandatory in Europe from 31 Dec 2010. After this date, banks will have the right to deny payment if a swipe&sign transacation has been done using a chip enabled card.