A wired ethernet shield and an Arduino WiFi shield are more or less compatible; one thing: you can't set a fixed IP address for the Arduino Wifi shield (a server with a changing IP address is a bit clumsy imho). The software for that other shield (Async Labs) is a mess because of a total lack of documentation (at least I haven't found it yet). It is based on a uip (micro IP) stack and there is a http server (or client) written on top of it; the uip stack comes from a Swedish university (according to the code itself). It should be possbile to use TCP sockets but I don't know how (due to the lack of that documentation). Software wise the best solution (for me at least) is an ordinary wired ethernet shield and a tiny wireless router ... but I'm open for any other acceptable solution 
kind regards,
Jos