Bill, you are correct in identifying which algorithms are used by which software. I do not actually know if Smart Sharpen has changed between CS3 and CS4 (sorry, I don't work in that area of the code). Nor have I attempted to use its methods for the purposes of image resampling (e.g., for large-scale upsizing).
Theoretically all "linear" filters, such as the cubic, Lanczos, etc. filters commonly used for resampling (including all the variants offered by software such as ImageMagick) will tradeoff in the areas of blurring, aliasing, and ringing. Blurring is obvious: if a filter blurs too much then you lose detail. Aliasing can generally manifest itself in terms of unwanted jaggies along edges, as well as false patterns (e.g., Moire patterns in fabric or window screens). Ringing generally shows itself as the presence of multiple dark or light halos surrounding a high contrast edge. It is theoretically impossible to eliminate all 3 with a single linear filter of this design. That doesn't mean you can't get good visual results, however.
More sophisticated filters can be used for the purposes of image resampling. They can in some cases produce superior results for large blowups. In general, however, they can in some cases produce unnatural (err, non-photographic) artifacts at the edges, and it can be hard to predict on an image-to-image basis whether you'll get one of these or not. (One "advantage" of a linear filter such as the ones described in the preceding paragraph is that they're so simple that it guarantees consistency from image to image ... e.g., if you get halos on one kind of edge, then you'll always see halos on that same kind of edge.) The other downsides of the more sophisticated filters are that they may not parallelize well, hence tend to take much longer to run (anywhere from 2x to 20x as long), and generally only make a difference for big upsamples.
In our view, most photographers tend to do image resampling using scales in the linear dimension of about 0.2 to 2. A scale of 0.2 is typically used when resizing an image down to web-sized display. A scale of 2 would be, for example, taking an uncropped 5D image and trying to make a 16" x 24" print at 360 ppi.