So here's why yoga can be* a good fit for me. I haven't done pilates, so I can't speak to that directly. But I'll bet many here are in the same situation as I am.
The other physical activities I do and need to condition for tend to be fast-paced and dynamic, with the focus necessarily on executing the activity itself in a way that is effective and fun and safe. These sports use the body, but they are not really about the body. While doing them, attention in the moment is not - and, I would argue, really cannot be - on the subtleties of where your body is tight or loose or weak or strong or whatever. Nor can or should it be on balancing those inequities. Instead it has to be on skiing through that next gap in Halloween Glade or on not riding off the edge of a narrow plank bridge.
It's because of this backdrop that I find yoga rewarding. It's a time to get stronger and more flexible, yes. But it's HOW I get there that I like. I love camping out in a pose and making the little guided adjustments and unguidable discoveries - encouraging or discouraging - that go with that. I also like the fact that I do it in one place and without a lot of gear or planning or other hoopla. I learn what I am or am not doing and what I can or cannot do with my body better in this context than I do while skiing or biking or hiking because I'm not distracted by wanting to get on with the "real" activity; learning is the activity. For me there is no agenda. I have no specific "goal," other than to fend off Father Time a bit. I'm just doing it.
*if I'm patient, practice frequently, and don't try to do too much too fast ... lots of "if"s, and I fail to implement more often than I succeed