Unlike some units, the civlopedia doesn't mention what real-life ship class the Destroyer unit is based off of. My best (amateur) guess is that it's an American or British design, possibly the American Sims, Fletcher, or Benson classes, or the British U and V, W and Z, or C classes. However, at this size and resolution it could also pass as some German or Japanese designs; there seemed to be some level of international similarities.
Most of the real-life ships seem to have rear guns, which the in-game model doesn't. This could be a simplicity/speed/laziness decision on by developers, or it could help narrow it down further.