I have tried the Russian 6N6P (stock), Russian 6N6P-IR, and Shuguang 6N6-T. Keep in mind that these tubes get extremely hot when operating, so when I'm comparing them among themselves or against 6SN7 tubes, I have to wait a few minutes before switching tubes. Also, the newly inserted tubes need about half a minute to heat up to operating temperature. I'm emphasizing these aspects because I don't have very good 'hearing memories', so it is entirely possible that some details in the difference is lost when I'm waiting/switching. So take my opinion with a grain of salt. Also, I used VE Zen 2.0 and HD 600 for the audition.
That being said, I believe here is a significant improvement in sound quality moving from stock 6N6P to 6N6P-IR, and again form 6N6P-IR to 6SN7. Also, the improvements are more noticeable on HD 600 than Zen, probably due to the change in sensitivity, among other factors.
The biggest improvement is the tonal clarity across the frequency range. The sound is just more crisp to my ears. Another big improvement is the reduced harshness in the treble. This is especially noticeable on the HD 600 where I have to turn up the volume. HD 600 can be fatiguing sometime, mostly due to the harshness in the high. This is the case before switching to 6SN7. With 6N6* tubes, the cymbals or high octave guitar will pierce my eardrum at the volume where I find bass and mid are appropriate. Also, the sound of the cymbals sounds muddled/distorted in some rock/jazz tracks. This improvements is less pronounced on the VE Zen. My theory is that Zen is a lot more sensitive than HD 600, and I don't need to turn the pot as high to produced the same perceived volume to my ears. The 6N6* tubes just won't hold up at a higher output level.
I have multiple sets of 6SN7 tubes, but I haven't gotten around to fully audition them all. I'll post my impressions on them later.