CC began as an outreach by Chuck Smith, at the time ordained as a Foursquare pastor, to hippies in the '60s. It always had as part of its mission to bring together diverse groups, and to be welcoming to various disaffected sorts. However in more recent years it has become more traditionally "fundamentalist," and some of Smith's comments could sound more confrontational than inviting.
The Vineyard began in the early '80s, when CC pastor John Wimber began embracing a looser and more experiential form of Charismaticism than CC found acceptable.
Both CC and Vineyard have considerable variability among local congregations.
CC has some explicit core beliefs and practices beyond the simple Statement of Faith. Good resources for interested parties are the booklet What Calvary Chapel Believes, by Larry Taylor; and Calvary Chapel Distinctives, Charisma vs. Charismania, and Calvinism, Arminianism, and the Word of God, all by Chuck Smith.
As for the Vineyard, beyond their generic SoF, you can probably find their stance on specific issues by obtaining materials from their publishing arm, "Vineyard International Publishing." In addition to various books, they feature official "position papers" addressing matters of controversy.
In addition to theological differences concerning eschatology and practical differences regarding the operation of spiritual gifts, the two differ on ecclesiology in regard to the roles permissible to women; CC rules them out of pastoral ministry, and in fact considers that point so important that it is part of their SoF, while the Vineyard accepts women as pastors (I know this because one of my female high school classmates pastors a Vineyard church in Ohio).