Yup, that's an alternative way of doing things. Your original version we would call pessimistic concurrency (I expect someone else to try to change the same data, hence I'll lock it). The version with a rowversion (don't call it a timestamp, that type name is deprecated) is optimistic concurrency (I don't thing anyone will change the data, but I'll check when I save, just in case)

You can do it with a row version, you can do it with a datetime column last modification date, you can do it by comparing the columns with what they were when you read the row. All work.