After trying to play it without pedal and stopping halfway through in discontent, I definitely go for -with- pedal. There are times where you need to let go of it completely (bar 29, the chromatic passage), but some parts sound best when you keep it intact for half a bar. Bear in mind that the pedal can give you wonderful crescendos without blurring (bars 35-36, LH run towards the bass F) and without sounding choppy, more like an avalanche of sound emerging from the piano. Blurring is more a matter of fingerwork, not pedal (of course, it takes a lot more fingerwork to get rid of blurring using the pedal...). A great way to keep the full sound and get rid of any blurs is half-pedal (ex: bar 9, full pedal at 1st beat, half-pedal at 3rd beat - the bass note stays, the volume doesn't chop down suddenly at the es1 (as it would if you changed the pedal fully) and it doesn't get louder and louder as it would if you let the pedal be, but fluently diminishes as you return to the C - all it nees is to be played pp all the way back down and it will come quite naturally... Just an example of what half-pedal can do.)
Playing the whole thing without pedal makes its sound very raw and severe, and it doesn't utilize the potential of the piece at all...
Just my two cents.