I realise this question was posed quite a while ago, but I happened to see it yesterday.
The reason for the sound quality difference might be because the KW1 introduces a 17 msec delay to the sound being sent to the subwoofer, whereas a direct cable connection involves no delay. (BTW the similar REL HT-Air product introduces a similar delay, 16-20 msec)
17msec doesn’t sound like a lot at first sight, but I know from my own measurements with REW that moving the mic a few feet can make a big difference to the bass response in a room.
The speed of sound is 343 m/sec or 1,125 ft/sec, so a 17 msec delay is equivalent to about 6m or 19ft - the KC62 has effectively been moved 19 feet further away when the KW1 is inserted.
So, to see what affect that has had on the response, if you can download REW to a laptop and buy or borrow a USB mic, like a MiniDSP UMIK-1, you will be able to check the frequency response with cable or with the KW1.
If there is any difference between the responses, I think it will be around the crossover frequency, where your LS50 W II and KC62 are interacting most closely.
Edit. I remembered that the user manual for the LSX II has a couple of interesting extras that don’t feature in the manual for the LS50 Wireless II:
From the KEF LSX II User Manual, p64:
The settings include:
• Desk Mode (On/Off, -10.0 dB to 0.0 dB)
• Wall Mode (On/Off, -10.0 dB to 0.0 dB)
• Treble Trim (-4.0 dB to 4.0 dB)
• Phase Correction (On/Off)
• Bass Extension (Less / Standard / Extra)
• Balance Control (L–C–R)
• Subwoofer model
• High-Pass Frequency (On/Off, 50 Hz to 120 Hz)
• Sub Out Low-Pass Frequency (40 Hz to 250 Hz)
• Sub Gain (-10 dB to 10 dB)
• Sub Polarity (On/Off)
• Are you using a KW-1?
• Subwoofer delay (-10 ms to 10 ms)
I don’t have a LS50 Wireless II. When you are setting up the subwoofer with the KEF Connect App, does it include the two highlighted items?