CC and the Vineyard used to be the same church, and grew out of the Jesus movement (1960s-1970s) on the West Coast of the USA.
By the 1980s the leaders John Wimber and Chuck Smith had different views on spiritual manifestations. John was all for them, Chuck had reservations. They split, the Vineyard became more spiritually liberal, CC became more spiritually conservative.
CC claim to embrace all the spiritual gifts but don't want them in their Sunday morning services, but say they are welcome at other times. In reality you probably won't see them very often at all, perhaps not at all.
At least you won't get the Charismania that's so prevalent nowadays.
Read up on their doctrines to see if they're the right fit for you.
And pray about it. It may be God wants you there regardless of doctrine.
peace,
Simon