The ratios aren't better, they are wider between 2 and 3 (that's what the W means). The W will have an intermediate shaft sensor that your current trans doesn't. Not a big deal, you can just ignore that because it's only for the adaptive shift control and your computer doesn't have that capability. The physical harness and connector is also different, you could rig that up since it uses the same basic system of solenoids. It would probably even drive but it would be forever stuck in limp mode and the od light flashing for all eternity.
Maybe it's possible to get the PCM tuned to make it work? Not sure never heard of anyone trying this.
I'm assuming you happen to have one of these things laying around because 5r55e's aren't rare or expensive so I cant see any other reason to attempt this. My advice would be to sell the w and find an e.