It depends on how sensitive the equipment you are working on is, but get ready for mixed answers!
Touching the case of a plugged in and properly grounded computer case is just as good, but only for a period of time.
The ESD keeps a constant ground connection so you don't have to worry about it. Touching the case discharges you, but if you become re-charged, you could inadvertently touch something and discharge to it. Personally, I've never used them, and have been building computers and servers for 20 years, and have never had a problem. I would just do smart things, though, like....don't work on computers while standing on carpet :) If you do happen to take a break, or something, and walk across carpet, just make sure you touch the grounded case or some other large hunk of grounded metal before continuing.