Wireless network range in regards to Xbox live question

I have an Xbox on the second floor of my house and the router is on the first floor (can't move it don’t ask). I have an original Xbox network adaptor whose antenna is kind of broke that is outside of the room that the Xbox is in. I just bought an Xbox 360 wireless network adaptor and hooked it up to the Xbox (inside room) and it has less strength than the older one that was outside the door and connected by an ethernet cable. So which would be better for signal strength, the older Xbox wireless adaptor outside my door, the 360 network adaptor connected by a usb extender to be outside the door, or a pelican network adaptor outside my door.