Jo Freeman spelled some of these differences out nicely in a 1986 PSQ piece. To wit:
The Democratic party is pluralistic and polycentric. It has multiple power centers that compete for membership support in order to make demands on, as well as determine, the leaders. The Republicans have a unitary party in which great deference is paid to the leadership, activists are expected to be “good soldiers,” and competing loyalties are frowned upon.
We found some recent evidence backing this up. In a paper I did with Richard Skinner and David Dulio, we examined the personnel files of the 100 largest 527 organizations to discover where else all those employees have worked. The links between all these organizations chart out different patterns across the two parties. The Republican network appears more hierarchical than the Democratic one.
Michael Heaney, Joanne Miller, Dara Strolovitch, and I found something similar in our study of delegates to last summer's presidential nominating conventions. We asked all the delegates to name the interest groups they belonged to. Democrats were much more likely to belong to an interest group. They also belonged to a much wider range of interest groups. Check out this graph, which shows how many delegates reported belonging to the top 11 interest groups in each party:
A bunch of Republicans belonged to just one group (the National Federation of Republican Women, as it turns out), with memberships dropping off quickly after that. Democrats are all over the place. Below is the networky depiction. The red groups are those which claimed membership solely by Republican delegates. The blue ones held only Democratic delegates. There are a few "bipartisan" groups, but their memberships are pretty one-sided. The key thing, though, is that the Republicans appear much more hierarchical; the Democrats have a much more horizontal structure of competing interest groups.
Update: Link fixed.