A good friend and I played with a 30-06 AI 47 years ago. All we had for powder was WWII Hogden surplus 4831 and some 4350, and we used RWS primers; they were hotter than standard US large rifle primers. We "borrowed" his dad's prized chronograph.
We couldn't get much if any "improvement" with 150gr bullets, 60-80 FPS more with 165s, and almost 150 FPS more with 180gr bullets. All bullets were Speers.
It convinced us back then that the '06AI was a distinct improvement with heavier bullets, only.
I've not tried one with our modern powders.