Basic Ecclesial Communities are nothing new in the Church. All the major religious orders - Franciscan, Dominican, Benedictine, etc, - have provision for lay members to meet and evangelise themselves and the world. More recently Focolare and Opus Dei have provided for these groups to include every member of the family.
None of these groups are themselves in competition with the parish, in fact, they provide a dedicated cadre for most parish activities. The concern with some of the more extreme BECs is that they seek to supplant the parish, as is happening in some secondary school communities which seem to be cutting themselves off from the local Church.