I've tried the "unfortunately, I don't feel the same about you" thing, and it often gets taken as a challenge. Frequently, the guy says "fine, we'll just be friends," and then proceeds to inundate me with messages, emails and/or phone calls. For me, the core of a romantic relationship is about the mental connection. If I don't feel the mental connection, I'm not going to ever feel anything else. There have been times when I've felt a spark of initial connection, but it has faded quickly once I've gotten to know the person better. That's an uncomfortable situation, and the hardest to "turn off." Sometimes I feel like my only option is to say, "listen, you irritate me, I don't want to hear from you anymore!" But it would be almost impossible for me to be openly mean like that, so in those cases, I *will* just fade away.
These are NT men, mostly. This was my experience when I was on POF several years ago.
Conversely, I'm pretty sensitive to feeling like I'm unwanted (lifetime of experience, perhaps), so it doesn't take much for me to drop it if someone fades away on me. It's possible there are times when I'm a bit too hasty.....although what has happened more often is that the person I've been talking to has found someone else temporarily more interesting/willing/whatever, and then when that doesn't pan out for them, re-opens the dialogue with me.