The key difference between registration in the US and membership in a party in Canada, as I understand it, is that the American primaries are considered part of the electoral law and therefore registration is part of the electoral law.
In Canada, political parties are private associations, governed by their own constitutions and bylaws. Internal party elections, such as nominations for the local riding, are governed solely by the party’s own constitution, not by provincial or federal election law.
Which is better? Well, the American system provides greater transparency, at least in some states, but on the other hand the Canadian system keeps the government out of the political activities of the parties. Personally, I think that the Canadian system provides for greater flexibility in the party system - it’s a lot easier to start a new party if you don’t have a lot of hoops to jump through, like socialxray’s example of the Green Party “finally” getting registered. Why should that be a big deal?
Contrast the federal parties in the two countries: the US has had the same two parties pretty much since 1860 or thereabout. In Canada, of the five parties currently represented in the Commons, two date from the 19th century, one from the 60s, one from the 90s, and one from just two years ago - and that one, the Alliance, is now the Official Opposition (i.e. - second largest). I’m not saying that the differences in electoral laws between the two countries is the sole reason for the differences, but I do think it’s a major contributing factor.
In response to Hari Seldon’s point - in the Canadian system, the leader’s powers over the nomination of local candidates will depend on the party’s own constitution. It’s not possible to say that the same principles apply for each party.
For example, in the federal Liberal Party, the leader can directly nominate a certain number of candidates in each general election, overruling the local constituency association. However, the constitution of the Canadian Alliance does not give the leader that power. I’m not sure what the constitutions of the ohter three parties provide.