i have never heard of the liberty program, but i've used ziPhone and have had complete success on my phone as well as my friends phone. Its so simple...and i'm talking as someone who jailbreak with the old method where it took 20+ minutes when following the instruction (jailbreakme).
iLiberty is more approved in the iPhone community, because many do not like Zibri, and feel he steals from other people, and as such, as received some ridicule. They both do the same thing, very efficiently. If you care about etiquette in the iPhone community, I suggest iLiberty.