One thing is Tx (Transmitting) and the other is Receiving..You have a receiving issue. Why increase the Tx power?..You need better reception.
Move around and see if you get a better signal or change antenna to a one with 9 dbi's. You could even use a portable directional antenna (yagi or grid).
I have the same Alfa and it has much better reception in BT than in WinXP. It comes with 5 dbi omnidirectional antenna.
The 1 watt power is for transmision..You have a receiving sensitivity issue...get a better antenna or move around to improve signal "reception".
You can also try changing the frec to 11mb, a much better frec to get more AP's..
I invite you to read about all this issues and the aircrack-ng suit.