Yes, there is a little, even between ISO and the International Electrotechnical Commission, or the IEC. These organizations work together in the sector. ISO and IEC have a joint committee, the JTC 1. Sometimes there is also a bit of competition between the major American standards development organizations, such as ASTM, which sees itself as a global organization that is equal to ISO. ISO, however, considers itself to be the only international organization. In short, I would say that this competition still exists.
However, I don't know about Europe.