Sorry for the late reply - I'm not on head-fi much these days.
I've had all over these except the HE-6SEV2 (and I probably won't end up purchasing one).
The 6 screw and 4 screw are much more alike than the HE-6SE was. Every time Hifiman has "rereleased" one of their classic headphones it's always sounded different. The HE-6se is probably the closest to the HE-6 when comparing the other "rereleased" Hifiman headphones. It captures a lot of the similar sparkle, but I suspect they did some of their diaphragm thinning.
Major differences between the original HE-6 and HE-6se:
-HE-6se is notably easier to drive.
-HE-6se has more bass and it tends to linger more (mostly midbass, not subbass)
-HE-6se has more treble overall and it starts peaking earlier
-HE-6 has better bass control
-HE-6 is more detailed
-HE-6 has a blacker background which gives it more attack/decay detail
-HE-6 is faster
-HE-6 has more midrange and less of a "U" shape emphasis
With the HE-6se I think a starting point to alleviate the treble emphasis is grill mod and changing out those stock pali pads.