If your budget says you can only have one, then of course you must choose. However, in my opinion, they really serve different purposes.
The best reason to have a camcorder is to record your kids. No still picture captures the hilarious motion and sounds of kids growing up. There are lots of other things you can do with a camcorder, but that's the only use I've consistently made of the camcorders I've owned. Editing videos is a hobby in itself. Its satisfying, but very time consuming to edit your raw footage into truly viewable "movies".
With a still camera, analog or high MP digital, you can capture and create images that have a depth and clarity not possible with any video camcorder. Another hobby/passion to consume you if you want it to.
For a single device to document a vacation or trip, I'd choose the still camera. Whenever I take both, I find I use the still camera most (even with my very small mini-DV camera).
Almost all newer mini-DV cameras allow you to capture stills, but not at very high resolution (often 640x480 max. but it's improving). Most newer digital still cameras allow you to capture MPEG video, in limited segments (30 seconds to a few minutes max). However, the quality of each formats secondary capability just doesn't measure up to that of the real thing.
my 2 cents...
BW