I used my headphones through both Kempers HP output, and my 2i2's HP out. To me there is a big difference in the tonal qualities right there.
Yep, different HPs sockets will drive a pair of HPs in different ways. it depends on their characteristics.
You might want to read this article, where the ideal coupling between headphones and a device driving them is described.
The specs for the Profiler's HPs out and your 2i2's HP out may be quite different. I'd try the monitors straight from both units, which are much less sensitive to th4e output's characteristics. If you perceive a much lesser difference, then it's the audio card's HPs output.
I need to drive my headphones at a certain level to bring out all the goodness.
Most probably, nothing changes in the rig's response at different levels (unless you clip something). It's rather ear's sensitivity that changes at different sound levels.
HTH