Water will run over a flat surface if it has somewhere to go, so a swale that is fairly flat will move water, however it could get deeper in some places as it builds up to move over a flatter area. Swales are typically used to divert water to where you want it to go. If they are fairly flat, then water has time to perk down in the areas where they run. A steeper swale will run water fast, and eventually erode over time due to the water action. Ponds are used to hold water, of course, but you can create swales that spread water out like a pond, but still keep it moving, depending on what you are trying to do with the water.
If you have ground that drains pretty fast, you could try tilling in some manure, light clay, or similar to help seal up the ground a bit. Bentonite (a clay) used to be used to line ponds to hold water in, but it can be fairly pricey, any clay will work pretty good, but you have to get it to the site, and get it worked into the ground, so there will be some expense there. You could also try a soil cement, which is tilling a small amount of cement into the ground, which will help move the water, but it may not soak in where you have treated the ground. This can be done with a normal rototiller. You only need about a 1/4 inch thick layer of cement for this type of thing, and then you have to water it enough to get good and damp, then spread it in the shape you want it, and then compact the shape, bearing in mind that the cement will want to start to harden once it is wet, but that small amount would take some time to harden. You would only really need to till it in about 4 inches or so.
Other options are lining the swale with some sort of impermeable material, such as plastic or
concrete. Old farms I know of in central and eastern Washington state sometimes used this approach. They would dig the swale, called a "ditch" in irrigation terms, and line it with the impermeable material if the ground soaked up too much water, and then used draft tubes to divert the water out of the ditch into smaller ditches (usually only an inch or so deep) which carried the water down the
hay fields, or other crop fields.
The newer system they use is a gated pipe, which is a pipe with a bunch of little openings that have a sliding gate that can be closed or open depending on how the farmer wants the water to move. The reason for the pipe is to cut down on evaporation.
Of course, those things all cost a lot of money, especially now with oil prices as they are. If you have animals, or access to manure,
Sepp Holzer uses that to seal up his ponds, if I remember correctly, and the same thing can be done with a swale. You could also try some sort of device to compact the swale, like a hand roller, vibratory plate compactor, or similar to help seal up the soil by compacting it.
We know that soils with a healthy amount of organic material in it will soak up water like a sponge and hold it for some time, so by building up your soils you increase the capacity for it to hold water. Depending on what you have under your veggy areas where you are diverting the water to, it may be laying there where you can't see it, but is available to the plants. You could try digging a small test hole to see what is happening down there.
What we are doing with our place, since we have so much debris left over from logging operations, is building swales with hugelkulture on the edges of them , where the
wood will soak up some water and hold it for the plants. Of course this will not happen over night. We have a mix of clay and sandy loam soils, but the loam has enough organic material in it that it holds a fair amount of water on it's own.
Hopefully you can find something of use in all that.
Good luck to you both.