It is impossible to change a cabinet from 8 ohms to 4 ohms by just rewiring it. You'd need new drivers.
The difference from 8 ohms to 4 ohms would be just shy of 3 dB, which *is clearly noticeable* - but not that much. About the same volume increase, roughly, from rolling your Master output volume up one notch usually.
I really dislike the completely false meme that is perpetuated on TB that a 3 dB difference is "imperceptible" or "barely perceptible" or "almost undetectable". I will tell you it easily detectable, no one would ever miss it. It is nevertheless not a great increase in volume- but to characterize it as barely perceptible is simply inaccurate. The minimum perceptible volume difference is 1 dB, sensibly enough.
You doubt me? I've posted this link many times, and no one ever seems to check it out. BassPounder, go check this link, listen to the audio clips that compare white noise at different attenuation levels from 3 dB, 1 dB (the JND - just noticeable difference level), and 0.3 dB, to and come back and tell me if 3 dB is "almost undetectable": http://www.animations.physics.unsw.edu.au/jw/dB.htm