First off, the AEBS has only one ethernet network port. The other is for the WAN input. And the signal can easily be split up with a hub.
Secondly, as someone else pointed out, the AEBS has a USB port for wireless printing to a select group of printers (although I hear tell of ones not on the list that work). This is a must if you are an all-laptop household. If not, and if you don't mind leaving one of your desktops on all the time as a print server, than that feature isn't terribly important to you. Just remember, if you want wireless printing in the future, that a 3rd party solution will cost you most of the difference between the Lynksis and the AEBS. In that case buy the AEBS now and enjoy it's ease of use and good looks.
Third, there are two flavors of AEBS, the cheaper one doesn't have a phone modem built in (so no wireless faxing, like you can on the high-end one) and no wireless access over dial-up if you ever move somewhere that doesn't offer broadband. It also doesn't have a port for the optional external antenna, although I've seen ads for antennas that will work with the cheaper AEBS but I think they require you to drill a hole in it.
Bottom line, if you think you want wireless printing, the AEBS is the way to go. If not, the rest of the stuff is not so important and you should go with the Lynksis.
Just my 2¢.