What information do you want to transmit? If he four bets, a player with another high pair will give less action later on. If three betting will not eliminate the blinds as well as reraising, then by all means reraise, but a far as table dynamics, we ought to be deferential to OP.

If you always 3bet/4bet with AA (or KK, etc.) then opponents will know you do not have them when you call, which can be dangerous. At 3/6 there are enough thinking players at a given table that if you remain for an appreciable amount of time, you will need to be concerned with the information you provide (especially when players record and spread data about players).

Also look what happens to the flop odds, with both raisers calling and blinds folding (both very likely in either case):
* as played: flop 10.5 SB minus rake
* if four bet: flop 13.5 SB minus rake
It becomes harder to give your opponents the wrong odds to draw after inflating the PF pot (straight out of HEPAP), which is not worth the extra 2 SB.

Therefore, mix up the 4 bet/cold call, with the table dynamics determining the ratio.