How do I show that I care to the same level about some random client?
I have had people fall asleep in the middle of my presentation (after lunch-heart medication). I have had people throw up in the middle of my presentation. I have had people cry in the middle of my presentation.
At that point, I stop politely. I'm not in sales mode anymore; I'm in human being mode. Maybe they need an ear. Maybe they need a beer. Maybe their staff understands that they fall asleep after lunch and that you can continue on.
Sales is mostly empathy and education. I'm selling to you because I believe that I'm going to make your situation better. If I reach a point where I believe that is not true, I'm going to stop selling to you, refer you to someone else, etc.
Occasionally, this loses me a sale. Oh, well. I generally engender so much good will when it happens that it almost always rebounds back to me later.