Do high level sub inputs really sound better?

You could give it a try but my experience says you'll go back to ICs.

Another vote for low level.

Some sub users (particularly REL) claim high-level inputs more effectively blend the bass tonality of the main amp with the sub. I prefer low-level inputs, valuing tighter control of LF I'm seeing from improvements in my preamp. But the crossover point is set low in my system and YMMV.

For a music only system, go with the high level inputs. I have tried both ways with my Martin Logan Depth, and the high level is a noticeable improvment. It integrates your speakers and sub better. And the sub does seem to keep up with the speakers much more. I remember several years ago reading on the REL site their logic behind it. And when I finally bought a sub and tried it, they were right.

High level means your amps are putting out the signal for under 20hz....IMHO and IME all amps sound better when not driven to the lowest. I would recommend using low level inputs and dumping the lowest freq. off from your full range amps.
Some subs have a line level XOver...I had very good results with Passive Line Level Xover, say from 50hz up!
You will win a lot of detail and dynamics on the mids and higher freq.
IMHO that is the most important feature of a subwoofer, leaving the lowest Freq. to a speialized sytem (the sub) in order to allow your full range system to breath better on top!