Hi Liz. Nice pictures, although that's the wrong ship in the picture. Same name, but the one in your picture was decommisioned (it used to be a nucleared powered ship, one of few that are not aircraft carriers, submarines, or ice breakers). It was a nuclear powered guided missile cruiser, similar in powerplant to the USS Long Beach, which was also nuclear powered.
The current USS Bainsbridge is an Arleigh Burke AEGIS Destroyer, and while it may not have a powerplant like the prior Bainsbridge had, in terms of weapons and systems and overall capability it is much better.