I found that when I switched to a DSLR from a point-and-shoot digital, the quality of my photos improved dramatically. Not because the camera made me a better photographer, but because the camera was more capable: less shutter lag, better auto focus, etc. It meant that when I started playing with a single setting at a time, I could really concentrate on playing with that setting (let's say, shutter speed).
For instance, when I wanted to explore water photography, and how much flow was interesting, versus how much began to look like fuzz (and how slowly I could hand hold), I didn't have to worry about focus, aperture, or any of the other settings, knowing the camera was competent to take care of those settings. When I've tried this on point-and-shoots, I've always come up with far less satisfactory results. It's not that those cameras can't do it...it's that, in my experience, they don't.
I'd argue against using film as a learning tool. The greatest thing about digital, to my mind, is the lack of a per photo cost. That means you can experiment freely (so to speak), and learn a huge amount about what doesn't work. Of course, that means you have to go through all those photos, look at what you did (another advantage of a dslr is that it tells you what settings you used for a given photo), and critique yourself harshly.
For me, really trying to learn with anything less than an SLR was an uphill battle, and I think it's a necessary tool (especially for someone who's learning). To take great photos with a point-and-shoot requires a much better photographer.