The first example you mentioned (i.e. the one to /api/management/feeds/create) is using the Feeds Management API; it looks ok to me on first glance... can you share the error message you got when invoking it? You should be able to see logged request/responses in the Admin > API Keys as well.
The second example you mentioned (Feeds_CreateFeed) is using the Native API, which we don't really recommend if there's an alternative available. It is basically a wrapper around stored procedures and the database. But in this case, it looks mostly correct, but the FeedType_Name is wrong; if you look at the Feeds table in the database, you'll see a universal feed is actually called ProGet in the database.
Anyways, please use /api/management/feeds because it's easier to use and won't change if we update the database or stored procs.