Less private than cash. Every transaction is public forever, and if your name gets linked to one address, others can often trace your activity.
Go deeperThe biggest link is usually an exchange that has your ID. To improve privacy, use a new address every time, run your own node, use your wallet's coin control to avoid mixing coins from different sources, and use Lightning for spending. Some privacy tools, like CoinJoin, exist, but check the laws where you live, since some privacy services have faced legal action.