MacBook Pro creates soft hissing sound through headphones
Tough to know for certain, but my money is on an impedance mismatch between the output of the Macbook and your new headset. Or, perhaps more accurately stated, excessively sensitive (low impedance) headphones are revealing flaws in the MacBook audio output circuit.

Care to share the model of headphones you're now using? My guess is it's a low-impedance model intended for use with portable audio devices.  You can boost the impedance by adding an in-line volume control adaptor like the Shure EA650. You will find other suggestions for solving this problem, including some DIY answers, by searching the forums at Head-Fi.org

For more information/background see: Impedance, and how it affects audio equipment by Rod Elliot and Sound On Sound: Understanding Impedance.



Another possible solution:
I have M-Audio powered monitors plugged into my MacBook Pro, and plug my Etymotic earplugs into the headphone jack on the monitors for private listening. I haven't noticed any noise problems with this set-up.