I've often touted the efficacy of Barnes TSX in my 243. I'm definitely a believer and something of an evangelist.
The only two objections I hear to the use of copper/non-lead ammo is either political (they're trying to control us/ban hunting/etc. etc.) or cost (store-bought factory ammo is expensive.) I used to buy into the political argument, and I'm not dismissing it, but I found it irrelevant once I realized just how effective and accurate the Barnes TSX ammo is. If more hunters realized this, there would be little need for laws banning lead ammo, because the industry would move that way in response to consumer demand. I recognize that factory ammo is expensive; I just bought a box of 308 for a friend for $57. Compared to Remington Core-Lokt or other basement price (and performance) ammo, that is super expensive. Compared to other premium, high performance ammo? Not so much. (Nosler, GameKing, Federal Premium are all comparably priced.) Additionally, when one calculates the total cost of a hunt, ammo is probably the smallest line item on the receipt. (My single biggest expense last year was fuel for the truck and the side by side. My 2nd largest expense was Mountain House.) This is doubly true if one prorates the sunk cost of big ticket hunting accessories (side by side or 4 wheeler, rifle, scope, etc etc) over many years.
So with all that said, the one drawback I'm beginning to see after shooting Barnes TSX for 5-6 years now is that the bullets are usually (but not always) light for caliber. The only thing that might drive back to traditional lead ammo would be if I found a projectile that a.) had similar or at least acceptable performance, and b.) had a significantly higher BC that would extend that effectiveness further than my current bullet. The rapid loss of velocity downrange is the only limiting factor.