The answer is no.
As previously mentioned, too many other variables to define any tangible difference in bullet performance.
ProHunter and GameKing are the same bullet in terms of fundamental construction. The differences were explained by the Sierra Technician by email as:
When it comes to the same weight and same diameter, like your #1560 and #1540, the two bullets are made the same way with the same components. This means we use the same style of jacket surrounding the same style of lead core and the process putting them together is the same. The only real difference is the shape of the bullet and by adding a boat tail to the rear of the GameKing, it gains BC numbers. Because it is more efficient in flight, it doesn’t slow down quite as much through the same atmosphere and will therefore hit a target at the same distance a little faster. At the range you are taking animals, the bullets are still going a similar velocity on impact so I’m not surprised you’re seeing similar results. Every now and again, I’ll get reports that our GameKings are more fragile than our Pro-Hunters (with all other things theoretically equal) and my theory for a reason is because there is less bearing surface on a GameKing. This gives the lead core less friction to lock into the jacket with, giving the impression it expanded quicker in relatively similar hunting situations.
At normal UK hunting ranges, the differences identified above would be masked by point of impact, animal size, animal position. I've used both in 150gr for years and do not notice any difference other than a modest improvement in drop at 300m in favour of the boat tailed GameKing.
Nigel is right, the 180gr .30 cal is a big step up in jacket thickness and toughness. The 165gr .30 cal sits between the 150 and 180, as one would expect.
They are fantastic bullets, The only reason I've stopped using them in .30 cal is because the price here has gone through the roof, and the Speer does exactly the same thing for half the price.