I honestly don't think you'd be interested in my honest answers to your questions. JRiver isn't doing any of the things you're asking about, unless you specifically enable DSP settings. Maybe you have DSP or equalizer settings turned on in Winamp that makes it sound better to you. When you say "I just use whatever it uses" it doesn't sound like you've put a lot of effort into understanding all the intricacies of audio reproduction in Winamp (or JRiver) so to an observer like me there's the possibility there's some configuration in play you're not describing or not experienced with.
The thing is, sound isn't sound. Accurate reproduction is one thing, and it can be measured. What sound really is, is your perception of it. That can be tested, but not measured. Everyone's perception is different, and you like what you like.
Some people like the sound from Bose speakers. They are notoriously inaccurate, but some people think they sound wonderful. That's fine.
JRiver reproduces music accurately, your system does not. You prefer the sound of Winamp through Directsound.
If you were interested in accurate reproduction, you could be told how to configure for that. But you want something inaccurate that sounds the way you want. That's fine. To each his own. But there's no formula for "make this sound the way I want."
As I told you, go ahead and set JRiver to DirectSound, and it will sound more like Winamp. Make the volume the same, turn off all the DSP on both and then they will sound exactly the same. If you do that and still think they sound different, have someone blind test you between the two, and I think you'll find you can't really tell the difference, because there isn't one. The mind is a powerful thing.
If you want to use JRiver, fiddle with the DSP until you like the way it sounds, and enjoy your music.
Good luck to you.