I hunt specific bucks. I have always loved big antlers and tried going after them. While I have had some fair success with that I pretty often settled on the buck I killed for no other reason than it presented the opportunity. I've killed a lot of good bucks when I knew there were bigger bucks around. As they say, a bird in the hand is worth two in the bush.
But these days that doesn't do anything for me. I don't get a kick out of just any good buck. I decided to challenge myself to pitting against only the oldest/biggest buck available to me that year, ignoring all others. So that's what I do these days, for the most part. And I'm loving deer hunting again like I did when I was a teenager. It's fun. I fail a lot but I succeed enough to keep me chomping at the bit. And probably even more than killing something, I enjoy things I learn by playing that cat & mouse game. Each buck is like it's own puzzle to solve. I guess if I had to put a number on my success rate it would be somewhere between 30% & 50%. I normally hunt TN & OH and between the two I usually tag one target buck. Sometimes I'm lucky & fill all three tags. Sometimes none. Failing doesn't bother me much. If anything it drives me to strive harder.
That said if a random bigger/older buck comes in range than my target buck, I'd probably kill it. It's never happened so I can't say or sure, but probably. I also occasionally hunt other states and when I do that I don't have history with bucks. All I can do is scout a spot that seems like I might see an older buck, and then if given the opportunity I shoot the first older buck that presents. That's a whole lot different than hunting my private grounds where I have bucks that I've seen for years & know exactly how old they are. I enjoy both types but really enjoy targeting specific bucks.