To understand which instrument will be most suitable let us have a look at two typical scenarios:
Scenario 1: You are the head of a production line of electric devices. During the production process, you are checking parameters like Voltage, Currents and Power to make sure the produced parts are okay. Or you want to do some brief troubleshooting. No deeper analysis is required, just a quick check because at the end of the production line every product will undergo a detailed test. So you are looking for a quick and cost-effective power measurement solution. In this case, a power meter is fully appropriate to do this job.
Scenario 2: You are a test engineer who is testing electric drive trains of cars, trucks or other vehicles. You do not only want to measure, but you also want to store raw data to analyse them further. As well you want to get some real-time analysis to be able to increase the efficiency of the drive train. Such a high-end measuring task requires the usage of a power analyzer.