Just for giggles, I put the two music videos together here and I can see some aesthetic similarities between them such as the closeups of the emotive faces shedding a tear from the right eye. Aside from that (and only sartorially speaking), well, Miley swings back and forth buck naked, monkey style from a wrecking ball while Sinead is dressed all in black from head to toe. In black. From head to toe.
Check out the two videos. If you wanna know more about the brouhaha (oh, there is more!), I have included a few links of interest below.
Image source and more about the hullabaloo