Bergkamp is no more qualified to be a coach than Vieira, but Vieira is more outspoken and perhaps a stronger character (and leader)...that doesn't equate to him being a better manager but at this point it's all we have to judge them on.
One things for sure, if Bergkamp became manager he wouldn't harp on about being in the CL for X years due to his fear of flying. Probably prefer to be in it once and win it!