While the above is technically accurate, I'm not sure that it communicates very well. So I decided to stop being wishy washy and just show straight up what I'm talking about.In favor of Zerene Stacker, it gives cleaner images (less halo & stacking mush), especially for deep high magnification stacks. If you are interested in stereo/rocking 3D views, then another difference is that Zerene's method works well for all subjects, where Helicon's method only works well with smooth opaque surfaces.
Regarding halos, here's the same stack processed through ZS PMax and HF Methods A and B. These are unretouched and unmodified, processed with default parameters in all cases, using current versions of both programs. This is the head of a fruit fly, shot through a 10X microscope objective, HERE.
Regarding stacking mush, here's the same stack processed through ZS PMax and HF Methods A and B. These are unretouched and unmodified, processed with default parameters in all cases. Subject is the papillate stigma of a maple flower, HERE.
Here's an example with issues in both stacking mush and halos. It's a pair of dandelion seeds, shown in their entirety HERE. Processed through ZS DMap and HF Methods A and B, unretouched and unmodified, processed with default parameters. (The undersides of both seeds and the OOF background between them are good places to consider.)
Regarding stereo, here's the same stack processed through ZS PMax and HF Method B (the only that supports stereo output). Again unretouched and unmodified, processed with default parameters, except that for HF I've selected the highest quality surface. Subject is a hobo spider, HERE.
If you don't immediately see the difference in these pairs, then consider the bristles on the front legs. In the HF image, some of the big bristles are simply missing, and the rest of them look like they've been greased back against the cuticle or are streaming off the legs and pointing back toward the balsa block. This is a fundamental characteristic of the 3D surface approach used by HF. If your subject really does have a smooth surface with no overlaps or discontinuities, then the HF approach works great. If the subject does have overlaps or discontinuities, then the 3D surface approach does what you see here.
I have the usual conflict of interest in this post. Because I wrote Zerene Stacker, I imagine the reader will presume that I've somehow fudged the demo to make ZS look good. I mean, the comparisons are pretty striking, at least to my eyes. But nope, no fudging -- everything is exactly as stated.
What I have done, I frankly confess, is to deliberately choose subjects that illustrate what happens outside the range where Helicon does well.
This approach goes directly counter to reviewers' common practice of choosing some easy subject that every software handles well, and then structuring the review as "well, they all do great work, so let's talk about other stuff".
The reason I choose to make the comparison like this is that these are the sorts of subjects and issues that I have faced from Day 1 in my own photography.
I've used Helicon Focus since 2004 (before it even had image alignment, let alone retouching). For a long time I recommended it as "best of breed". It's a great tool for a lot of purposes.
However, the roots of Helicon Focus appear to be firmly planted in what to me are "shallow low magnification stacks", with subject field widths of a few inches and larger. When used with deeper stacks at higher magnification, it develops the issues shown above. At the same time, the design of its retouching capability becomes less effective because depth navigation is slow and all you can do is clone from source images to a single output image.
It was exactly those considerations that prompted me, in 2008, to begin development of a new tool designed from a clean start to focus on the stuff I cared about: deep high magnification stacks.
Zerene Stacker is the result. It's not perfect, but for what I do it's a big improvement. Your mileage may vary.
Hope this helps. At least now you'll know for sure what I'm talking about.