I suppose grad filters can be quicker for those who don't like to spend post-processing time on the computer. If you have to get your image with a single exposure they can be a big help. I'd rather spend a little extra time at the computer instead of having to mess with grad filters while shooting in the field, but that's largely a matter of personal preference.
The biggest problem with grad filters is the lack of flexibility in placing the transition zone. With a level horizon it's not really an issue; but when you have an uneven horizon the use of the grad filter becomes more obvious. Mountains, trees, and other object that stick up into the sky end up getting unnaturally darkened. Depending on the filter strength needed, this may not be too objectionable, but for some compositions it just looks awful IMHO. Film shooters didn't have much choice (especially when shooting chromes), so they learned to deal with the limitations (favoring certain composition types, passing up on certain scenes with the dynamic range is just too great and a filter won't work, etc). But with digital we have additional options.
When digitally blending bracketed exposures, I have much more flexibility and control over how to do the blend. There are several techniques that can be used, from simple layers with gradient masks, to automated processing such as HDR or exposure fusion, to completely manual blending with layers and complex masking (or any combination of these). Yes, some image types will take quite a bit of work to get a truly seamless result; but those same images are the ones where getting a seamless result with grad filters is impossible.
Movement in-between bracketed exposures can be a problem when using just HDR Tonemapping or exposure fusion. But with the manual, layer-based approach that I use most often it's rarely an issue; only when the movement takes place in the 'transition zone' do you have a problem, and even then it can almost always be fixed with some careful masking (or as a last resort, cloning).
Moving water can usually be handled quite easily in the case of streams, rivers, and waterfalls. Exposure fusion handles these situations pretty well in most cases. For the cases when it doesn't (rolling waves on the coast, for instance), it's just a matter of making sure those areas are masked so that they come from a single exposure.
The hardest part of manual exposure blending is when you need the transition to occur in an area that has high-contrast edges. Simple exposure blending with masks or gradients will often produce halos or other unwanted effects. HDR Tonemapping also has problems with halos. Exposure fusion usually comes to the rescue in these situations. Exposure fusion as found in enfuse or Tufuse Pro essentially does pixel-level exposure averaging that's weighted for mid-tones. (That's a gross over-simplification, but you get the general idea). This works very well for high-contrast edges. Often times what I'll do is run my bracketed exposures though Tufuse Pro to generate my 'base' layer, and then use the original exposures as additional layers with masking to improve the overall image. Using the Tufuse image as the base layer makes getting seamless transitions between exposures much easier.