I don't know if you would call it basic... but protons are being constantly pumped into the intermembrane space causing the pH to decrease. This allows for a high proton gradient which allows the ATP synthesis.
I would call matrix more basic than the intermembrane space. But not sure if it is actually basic.
There is a nice diagram here:
http://en.wikipedia.org/wiki/Oxidative_phosphorylation
You can see that the intermembrane space is accumulating protons.