I did a bit of reading for you, but I'm not a catholic, so there were elements of difference between mainstream catholic and neocatechumens which were totally lost on me as I'm not up with a lot of catholic theological terms.
From what I read, I understand its a movement that believes a number of pagan and old testament practises have gotten into the catholic church over time which distract from the total saving power of christ.
They're not big on priests being mediators (Christ is our only mediator) and believe that members of the church are gifted with roles of pastoral care and evangelism too (you'd call them lay preachers, I guess). Their own priests are "catechisers"? and sound a lot like teachers. They still administer the sacrements (and believe in the catholic doctrine of transubstantiation) but they believe they sustain a person on their walk, rather than actually convert them??? (I'm a bit hazy here)...
from what I can tell - they believe one comes into relationship with God through a unique conversion by the Holy Spirit and that this conversion experience is not limited to the catholic church. They believe that any people who have entered a repentant relationship with Christ are members of his flock, and for that reason, they are prepared to convert catholics who they see are not in this relationship/are just pew sitting.
There was something about adult bapism and evalgelism by fellow believers having much more of a central place in the early church?
One fellow I read said their idea of free will is much more like Luther and Calvin's idea of total depravity; that we're totally unable to save ourselves without God's intervention but that once truly saved, we cannot fall away...so I guess they don't see themselves as needing to ongoingly earn their salvation, so much as secure it??
There was a bit of debate about whether they have been accepted by John Paul2 and Benedict, as a papal letter implies. Certainly, JP2 said mainstream catholics should meet and fellowship with them.
They're one of the fastest growing catholic (sects? I don't know whether that's the right word) in the world and the archdiocese of Sydney recognises them. They have a big ministry with the poor, especially in founding home, Spain. There are a lot of authors who think their ideas on priesthood etc are heretical. And I *think* they reject the council of Trent.
Please, anyone correct me if I'm wrong on the catholic or catholic neocatechumens on any point - I found it really interesting looking into this.