Part of the issue and prejudice for me was Speer bullets - this was awhile ago. The flat based bullets were "Hot Core" and the Boat tails were not. I think they still may be that way. So back then I avoided boat tails.
Fast forward a few decades:
I have a couple of rifles that shoot flat base bullets much more accurately than boat tails - a couple 30-06's and my Savage 99 300 in particular. In the Savage the difference is about three times the size of groups with boat tails. In my '06's it isn't quite as pronounced. But a couple are able to shoot very small groups with flat based bullets.
I suppose it really is a moot point for my deer hunting as I rarely shoot deer at more than a hundred yards and 1/2" groups or 3" groups wouldn't make a difference. But for antelope I often will shoot much further than that.
As far as performance on game since those days when I was younger, I have not noticed a difference. Perhaps when I did see a performance difference, I didn't see it as a boat tail vs. flat base bullets issue, but just a certain manufacturer's bullet - I believe that is more valid than flat vs boat tail.
