Basically, if he is 4betting QQ/AK, you need to put the money in here. 4bet/folding QQ/AK is pretty terrible as you usually have the correct pot odds and equity to call it off when you get shoved on. I'm not checking the pot odds for when you shove here 150bb deep, but I wouldn't think of 4betting QQ/AK and folding to a shove here. And to do so blind v blind would be even worse, because as I said you should be 3betting a fairly wide range in this spot, and if he recognizes this, he should be 4bet bluffing some % of the time.

So if he is 4betting QQ+, AK, that is his value range, and he should be calling a shove with that entire range. If he is only 4betting KK+, then you should fold as you are behind his range.

If for instance, he IS 4betting QQ+, AK and folding all but KK/AA to a shove, we are still going to profit from our shove with him folding 14 of 21 combos, or 66% of the time. So it would still likely be +EV to shove if he is 4betting QQ+, AK and folding QQ/AK to a shove here. Which is going to be pretty terrible because against your entire range he will have like 40% equity at the least if he was to call. But instead, if he 4bet/folded those hands he has relinquished his entire equity, so we win the entire pot 100% of the time. Which is obviously great for us, but terrible for him.

And that to the fact that flatting here are going to be in some bad spots on some flops. Remember you don't just have his range to worry about, but you have to worry about what he thinks your range is. How do you expect to get any more value from AK when he whiffs? What about QQ when a K or A drops?