A 'bike computer' is a generic term for everything from a simple wheel sensor giving distance and speed, to an all singing all dancing computer that measure cadence, speed, altitude, heart rate, power and anything else you can think of
A power meter measures the power you are outputting, and is one input into a bike computer. Power meters are expensive - a basic bike computer is less than $10, last I checked the cheapest power meter was worth more than my bike. They are also useless without a 'bike computer', but come with one - the computer with all the other sensors a typical bike computer has is the cheap bit.
Power meters, like HR monitor in the 1990's are a great tool, but that is it, they are only a tool. Think of TV sales channeled selling fitness gear -'but wait, there's more.... You too can have a 6 pack and a gorgeous girl with just one ride a week with your power meter. *In conjunction with a nutrition program *Result will vary, Not all users will achieve the same outcomes shown in the advert.'
If you don't know how to use them, have no interest in sports science and physiology and no desire to learn this stuff, they are expensive paper weights that slow you down. If you are prepared to learn and interpret the results they provide, they can be a great benefit.