It should be said that you really don't give up all control with the HV20 though. It will do 24P, which is most decidely "unvideoy" looking -- so long as you keep your shutter speed locked at 1/48 or higher in conjunction with the 24p.. I mention that because one of the main things that makes video look like video is a shutter speed equal to or slower than your frame rate. That's not really possible with film, as a shutter speed equal to the frame rate would mean the shutter is open 100% of the time, so a speed slower that the frame rate would mean the shutter is open greater than 100% of the time, which is physically not possible, but with the magic of digital it can be made to work. Anyway, the point is, shooting at 24p will mimic the motion of film, and keeping your framerate locked at 1/48th (which would equate to a 180 degree shutter angle on a film camera meaning the shutter is open for half the time the film frame is in the gate) or faster -- but preferably just 1/48th unless you're going for a "Saving Private Ryan - Storming Normandy Beach" effect. The faster the shutter speed, the smaller degree shutter.. so for example, at 24 frames/sec, a 1/120th shutter setting would equate to a 72 degree shutter on a film camera. It would give the slightly random strobing kind of effect as seen on that beach scene in Saving Private Ryan..
Of course, depending on what you're after a fast shutter may be ideal. I know the HV20 will do up to 1/2000th of a second shutter speed. Which if you were shooting with slow motion in mind might be a good option. For that I'd probably shoot 60i footage with a very high (1/1000th or 1/2000th) shutter speed, then convert that to 60p in post and play it back at 24 frame/second to match the speed of the rest of the footage. But I haven't experimented with that, so don't quote me on that.
Lighting is really going to get you further in terms of your footage not looking like a cheap home camcorder than a more expensive camera. Also I think it should be stressed that the "simplicity and artificiality of lighting" you're referring to from old movies will take A LOT of light. Those films were almost all shot on a sound stage with thousands (if not hundreds of thousands) of watts of light.
But again, the internals of both the A1 and the HV20 are identical.. same sensor, same chips, etc.. the A1 is a bit larger package that offers a bit more manual control, but essentially the same control can be wielded over the HV20 -- it's just a little less intuitive. Either camera is going to give you great images IF you properly light your scenes and shoot it in an intelligent way. Just grabbing a camera, turning it on, and maybe using a couple thrift shop lamps might look OK, but it's never going to look as good as an image that's properly composed, and properly exposed.
DV generally needs to be lit with more light than film. Not because it's harder to get an image -- most cameras will shoot in relatively low light. But because the latitude is so much smaller with the digital format, you have to pump a lot of light into your shadow areas and keep things pretty evenly lit to prevent noise, grain, etc.
As knightly touched on, the Shallow Depth of Field is based on the size of the iris and the size of the capture area. The smaller the iris, the more will be in focus -- regardless of capture area size. This is why with a pinhole camera everything is essentially in perfect focus regardless of the distance from the camera. The larger the opening in the iris, the less is in focus, however with a smaller capture area such as those used in digital video cameras, you can't narrow the depth of field much. There are a couple ways to do it though...
First, you can back far away from your subject, then zoom in to make them the size you want them to be in the frame. This will be helped by opening the iris up as wide as you can, and then stopping the image down with ND filters to keep it from overexposing. The nice benefit this has is that it will compress the image, so the background doesn't feel so far away, but it will also be blurred out a bit so the softer focus behind your subject will be pleasing to the eye.
Secondly, you can use a larger imaging plane. As knightly mentioned getting a camera with a larger imaging plane (CCD or CMOS chip) is going to get prohibitively expensive before you get quality results... so what can you do? Well, there are a multitude of 35mm adapters available. These will give you all the benefits of a larger imaging plane -- which basically is that it allows you to get a nice shallow depth of field. But the cost stays relatively low, because your run of the mill camcorder that will let you lock the exposure, focus, and frame rate now becomes a pretty high-end machine.
So, for roughly half the cost of the A1, you can get an HV20 and a nice Redrock Micro, or Brevis Adapter.. that'll give you the same quality image, with the shallow depth of field, and money left over to get yourself a 35mm lens or two, and/or some lighting.
The only caveat is that the extra glass involved with the 35mm lens and ground glass focus screen will eat a bit of light, so you'll need to pump up your light level even more. That's why it's important to get the fastest lenses you can afford. People are constantly raving about the 50mm f1.4 nikon lens to use with these adapters.