Students appreciate having the group test prior to the individual test. The above answers are for calculus courses only. It builds rapport between students and between the students and me. I often sit down for a few minutes with each group. After I get to know them, the lectures become more free-wheeling and they interrupt to ask questions when they cannot follow.
Major projects constitute a significant part of the grade in some cases.
Otherwise I do not use group grading. I ask students to grade their fellow group members in the hope of becoming aware of unequal participation. Students invariably prefer group portions to the testing, even though the results do not seem to be significantly different that the individual portions. I sometimes give a problem on the individual portion that had already appeared on the earlier group portion, at least in part. Or an individual problem may focus on one aspect of a larger group problem.