O2 uses the same infrastructure but has use limits, if you can get a cheaper deal with Be (they used to be massively cheap) theres no reason to go with o2.
I so nearly went with BE, but since I have an O2 mobile, O2 offered me 6 months free internet, which BE couldn't match. The only limit is the download cap, which is 250gig a month on my package. I've never come close to that.