Some thoughts, not sure if that will help.
I agree with KW71, the rivers looks a bit like a canal. It's not a bad thing because it's probably simpler to start this way, but they sure looks man made. I was wondering what parameters could be used to make them looks more natural.
So far, I see a big difference between streams and large rivers. The smaller a river is, the lower it's impact will be on surroundings. As a result, streams will typically "dig" into the terrain rather than have large banks, especially because the water flow generally faster in these.
Here is a small example for a tiny one:
However, the aspect of a river is really dependent of the type of terrain it is on.
This one sits on a rock bed. As it can't really dig into it (especially with some types of rocks), so the stream is larger and not very deep. There are still no banks but rocks are really visible. I guess it's almost impossible right now to handle these two types of rivers, because it will need a lot of local parameters. But something between these two seems good. The most important is: almost no banks/transitional area, and visible rocks, low depth water. Like that:
Or that one:
The larger the river is, the larger the bed becomes and banks start to be more visible. You can expect a large transitional area between normal terrain and the river bed, and the river banks are generally made of pebbles, sand and some dirt, most of the times mixed together:
The river is also deeper. The big problem here to make it looks natural is that these areas are never consistent in terms of symmetry. You never see a straight bank, sometimes a tree will grow in the middle, sometimes there will be a large patch of sand and dirt in the middle of pebbles. And most importantly, a river never has symmetric banks in terms of width. It can work with a straight line river, but as soon as there are meanders, you can expect a large bank on one side, and almost not on the other side.
At the end, I think border/transitional and depth parameters should be proportional to the river width. If you manage to add procedural rocks in it, it will probably looks more natural. The big question is the symmetry one, because I guess it's something really difficult to do with the current vector system.
That being said, I think that as an alpha state new functionality, it's already an impressive addition to the engine