I've used Visa Signature concierge a couple of times and have found it to be very 'meh'. The last time I called them they seemed to have limited the scope of what they'd do to making reservations and travel arrangements.
Visa Signature concierge is very meh in comparison to the amex platinum from my experience. (I've not used a centurion concierge, though reportedly it's the same service - I find it hard to believe that they're treated with the same service level considering the requirements and fees to be eligible for a centurion card, however)
The Amex concierge team has been able to find me items at local stores when I needed things ASAP that I was having trouble finding, and also managed to snag me a limited release item that was only available at the companies' location. (That was expensive, but still less than I saw them for being resold for online. I imagine a courier service could have been used if I was familiar with any in the area, since it was basically a 'drive there, pick up, drive to UPS store, ship' type request)
The Amex concierge team has been able to find me items at local stores when I needed things ASAP that I was having trouble finding, and also managed to snag me a limited release item that was only available at the companies' location. (That was expensive, but still less than I saw them for being resold for online. I imagine a courier service could have been used if I was familiar with any in the area, since it was basically a 'drive there, pick up, drive to UPS store, ship' type request)