Logan: Nature made me a freak. Man made me a weapon. And God made it last too long.
Donald Pierce: Charles Xavier, the world famous mutant octogenarian.
Charles Xavier: Actually, I'm a nonagenarian.
Charles Xavier: I don't think Laura needs a reminder of life's impermanence.
Donald Pierce: Geez, Wolverine, seeing you like this, it just breaks my damn heart.
Logan: As soon as I rip it out of your chest, fucker.
Charles Xavier: Fuck off, Logan.
Logan: See, you know who I am.
Charles Xavier: I always know who you are, I just sometimes don't recognize you.
Charles Xavier: This is what life looks like: people love each other. You should take a moment.
Charles Xavier: Two days on the road, only one meal, and hardly any sleep. She's 11, I'm fucking 90.
Answer: X-24's healing factor is much weaker and slower than Logan's, and Dr Rice has to give him the serum to heal his injuries at the farm, so presumably he couldn't heal fast enough to survive the shot. It may also have been a different bullet type - the one in Wolverine didn't do nearly as much damage on impact. Makes sense that Wolverine would have possibly designed one to overcome any healing factor.