If you are choosing between a CRC and SHA1, you probably need to reconsider your understanding of the problem you are trying to solve. Those algorithms solve different use cases.
If you are choosing SHA1, now that it is retired, you probably should think harder about the problem in general.
CRC should be better for any error detection code issue. Faster to calculate, more studied guaranteed detection modes, and so forth.
SHA1 has no error detection studies. It's designed as a cryptographic hash, to look random. As it so happens, it is more efficient to use other algorithms and do better than random if you have a better idea of how your error looks like.
Real world errors are either random or bursty. CRC is designed for these cases. CRC detects the longest burst possible for it's bitsize.
