Well, "feeling strong" definitely gets harder when you're comparing yourself to riders that are more capable than you are. To me, it's not a competitive thing - it's how I feel when climbing a hill without any hesitation or dread. Others might pass me going up that hill, and I'm perfectly Ok with that. In fact, trying to keep up with someone who's out of my league definitely does NOT make me feel strong, as I'm pushing outside of my window of strength. Doing so helps move that window over time, but the benefit in doing so is that you can dial it back, and be able to crank it up over that hill or cruise along at a good pace on the flats with that feeling that you could do this for hours and hours. That is a feeling of strength, and is what makes pushing yourself to go farther and faster on a regular basis worthwhile.

Someone is always going to be stronger than I am, and appreciating my strength only in the context of comparing myself to others puts me at the mercy of that disparity. In contrast, being able to carry on a relaxed conversation while climbing a hill that would have had me hanging over the handlebars gasping for air a few months or a year or two ago is something self-contained and not jeopardized by anyone else's capabilities.

Then again, I've never been a very competitive person.