They're not any deeper than a GFI.
You can always add a "mud ring" to increase the box depth if you need.
I had a dual receptacle give out in our kitchen last year (bus bars inside would no longer hold onto the male tabs on a plug) and my wife wanted one of the USB/dual receptacles so she could plug in her personal phone and work phone without having to use the wall warts.
Since my house was built in 1955, all the original boxes are the not-very-deep metal ones. I didn't want to have to replace the metal box with a slightly deeper one, so I used one of the 1/4 inch thick plastic "mud rings" from Home Depot, along with a deeper Decora style wall plate and that worked out fine.
The other issue you may run into is that the older metal boxes, while not being very deep, are also not very wide!
If you buy any of the USB receptacles, make sure you buy one that will also fit the width of the metal boxes as well. Some of these USB receptacles have pre-installed wires coming out of the back, and some have side wiring screws for installing your own wires.
If you get one of the side wiring USB receptacles, be sure that when the wires are installed into the screws, that the screws will NOT hit the sides of the metal box! I ran into this situation with the box I had in the kitchen. It is not deep and it was just a bit too narrow to comfortably fit the newer style side wire USB receptacle that I bought.
Yes, it fit, and yes I could wrap some tape around the body of the receptacle to cover the screws once I had the wires installed, but I did not feel comfortable doing that "just incase".
So I returned the first USB receptacle and bought the kind with the pre-installed wires coming out of the back. This receptacle fit perfectly with the addition of the "mud ring", and there are no side screws to accidently come in contact with the metal box.
Just food for thought.
Oh, and if you are going to get a USB receptacle, make sure the one you get has the two receptacles and the two USB ports in positions so that all four things can be plugged in!
I found that the USB receptacles that have the USB ports in the center of the receptacle, positioned vertically, and more towards the outside of the two main receptacles, works best so that even larger male plugs on some electrical items still fit and will not come in contact with anything plugged into the USB ports.
Jim