I will start off by saying that I use both factory ammo and handloads. Been hunting big game for 39 years, and handloading for 37.
While I try to find a more accurate handload for most of my rifles, I own a few where the accuracy is such that I do not think that I can improve on it y handloading, as I am not the best shot to begin with. (Shake like a leaf in a high wind! And it is not getting better with age!) While I can attain sub-MOA accuracy from the bench, that is rarely duplicated in the field. I am confident that I can place a bullet accurately in the vitals within my range limits with various rifle/cartridge/scope combinations. Like any other hunter who has hunted long enough, I have missed, and lost a couple of animals over time. But I attribute this to me and my shooting, not the bullet.
I have used a number of cup and core bullets over the years with great success, including Winchester Power Points, Hornady Interlocks, Speer Hot Cors, Sierra Game Kings, and Nosler Partitions, from mild to magnum cartridges from 243 on up to 375 caliber. If I had no other choices, I would still hunt with any of these, and I still do where they are the most accurate bullet from a particular rifle suited to the game and environment that I am hunting. I too have seen instances where the bullets may not have killed as quickly and cleanly as they should have, even with good bullet placement.
As always, bullet placement is more important than the bullet design may be, given an appropriate caliber and weight, with the proper retained velocity and energy, is used for the game animals being hunted.
I have shot a few Bergers in a few rifles, and while they are accurate, my only instance of on-game performance was less than desired. Ultimately the animal died, but it ran farther than any other animals I have ever recovered with a well placed double lung shot, just above the heart. The bullet split and travelled in different directions within the animal, with lots of shrapnel on the onside ribs, a small part going out the opposite ribs, and the remainder going through the guts to the hind quarter. While only a sample size of one, it has kept from using them again on game.
I have also used the Trophy Bonded Bear Claws, Trophy Bonded Tips, AccuBonds and newer Terminal Ascent Bonded bullets. I have to say that the consistent accuracy, and ease of finding good loads quickly with the AccuBond, from .257 to .375 cal, and then the on-game performance (antelope to bison), has made it a favourite of mine, since it first came out. Where bullets have been recovered, weight retention ahs averaged above 90%, and expansion has averaged between 2 and 2 1/2 times the original diameter. While I still hunt elk with cup and core bullets from some rifle/cartridge combos, I prefer the bonded bullet for additional penetration performance should heavier bone be encountered.
While my experience with the Terminal Ascent is limited to 7 animals, all have been complete pass throughs and one shot kills. And the accuracy from several rifles has been MOA and better, except for one, where the accuracy is still acceptable for hunting. So far, I am impressed with it. I will continue to hut with them too.
As for the monolithic bullets, I have tried the Barnes X, and then the TSX and TSX bullets too, and the Trophy Copper. Accuracy hasn't always been top notch, but where it was, I did like their accuracy. I did take a moose with the older X bullet, but the kill wasn't as quick and clean as I would have liked...but could have been attributed to bullet placement rather than the bullet on the initial shot. I am looking forward to seeing how they (TSX) work first hand on bison from my 416 Taylor. From there, a Cape Buffalo???
The Trophy Copper accounted for a moose, where the bullet completely passed through it, and it only made 15 yards from where it took the shot.
I have witnessed a number of animals taken by others with the TSX/TTSX, Nosler E-tips, and GMX's. Many worked as advertised, but a few did exactly as others have experienced. For me, the jury is still out...but I will still try the Trophy Copper on more game, as it is the most accurate factory load in that rifle, and it killed quickly and cleanly.
It is good to have choices!
In the end, use what performs best for you in your rifle, and place the bullet accurately.
And keep your knives sharp!