All-in, they are both very good hands. AK does great against all hand types, dominating the other Ax hands and having around 50% against other pairs. It still has as much as 30% against KK, but a huge dog against AA.
QQ on the other hand, will be a huge favorite against other paired hands (beside KK/AA), and dominate all unpaired hands except AK. Ax or Kx hands have around 30%
equity against this hand.
After the flop, having QQ it is pretty simple to know if the flop is suitable to continue betting. Dry flop w/no overcards you will be well ahead the majority of the time.
With AK, hitting an A or K will put you ahead in most situations, but you will miss a lot of the time and be left with some difficult decisions.
For this reason, I prefer to have QQ over AK.