Laptops are less powerful than desktops in general. This is not always the case granted, but in general an equal specced laptop is slower than a desktop.
Wireless is bad because while the speed might be fine, wireless routers will always have spikes, and its the spikes that are the most aggravating. I'd rather play at 55 fps than 60 fps and have it spike every 10 seconds. Of course wireless is better than no connection, but if you have a choice, try to get wired.