At times when you would need to do some computations, you need to know if you have a clear idea of the different formulas that you are going to use in order to come up with the right answer. Between CRC and Checksum, you can already expect that CRC will have a more complicated way of computing. Expect that you are going to go through some complex computations in order to come up with the right answer.
The checksum can be used when you just want to detect some small changes in the data that you have gathered. CRC will be used when you need to find out some double-digit errors that you may have missed. CRC can be used when you are doing data evaluation.