You don't seem to understand what Chuck is saying.
Your question equates to 'which fruit is better: an apple or a sirloin steak?'
Expresscard is the little slot on the side of your machine, a little more than an inch wide. It's a generic port (kind of like a USB port, but accepting cards, not cables), that can be used for many things, like connecting a camcorder or camera, or perhaps connecting to the internet with a modem in that expresscard port.
An EDGE modem is used to connect to the internet, presumably over the mobile phone networks. You want to use this to connect to the internet. They come in different connection formats, such as USB and firewire, and yes, perhaps even Expresscard.
So try the EDGE option.
(Side note: EDGE is a slow connection really '2.5G'; much faster are the 3G USB dongles that mobile phone companies are selling.)