Resolution
Pixel resolution of zoomed systems
When you zoom an image out by 1.33x to fit a 2.35 screen you increase the size of the pixels both vertically and horizontally by one-third (4/3). This equates to a comparative resolution (between zoomed and original sized picture) of the square of the inverse of 4/3 ... 3/4 squared = 9/16 = 56%... or 44% pixel resolution loss at a fixed viewing distance.
Pixel resolution of anamorphic systems
When you use an anamorphic lens to optically stretch an image in only the horizontal direction, the vertical pixel size remains the same as before, with only the horizontal pixels increasing in size by one-third. This equates to 3/4 the resolution of the original non-anamorphosed picture, only a 25% reduction in resolution (compared to 44% with zooming).
Summary... with an anamorphic lens you only lose pixel resolution in one direction: horizontal. Overall, using a lens has the potential to give better pixel resolution than straight zooming, depending on the quality of the optics in the lens.
Picture resolution of zoomed versus anamorphic systems
But pixel resolution is not the only consideration. There is picture resolution to look at too. Picture resolution relates to the content of the image that is made up of individual projector pixels. Average picture resolution is usually lower than the projector's maximum pixel resolution. Think of a standard DVD projected out of a 1920x1080 projector: the limiting factor, as far as clarity and resolution of the final viewable image is concerned is the picture resolution of the DVD image (720x480 NTSC or 720x576 PAL), not the pixel resolution of the system (the 1920x1080 projector). Even Blu-Ray disks have very little (if any) full resolution detail in them. The pixel resolution, if higher than the picture resolution, may be wasted. Put another way, the total system is only as sharp as its softest component.
You will lose some picture resolution (as opposed to pixel resolution) via the digital vertical stretch (digital extrapolation) that you must use as part of the anamorphic lens process. How much this loss amounts to has been a subject of hot dispute here.
One recent study by Cine4Home showed that static test patterns - 1x1 pixel checkerboards, single-pixel vertical lines and so on - lost resolution due to the vertical stretch process. This is actually not a very startling revelation as a repeated 1x1 pixel pattern is the highest resolution a projection system can offer. There must always be some loss when that pattern is disturbed by stretching it, especially by a fractional value like 4/3. This resolution loss would also apply to video gaming and similar PC-based displays where single pixel resolution may be common, especially in fine text.
The question to ask is whether "real-life" viewing images with continuous tones and continuous detail (e.g. movies) have as much noticeable loss of resolution as their static counterparts?
As a first consideration, most of the detail in a movie is at a far lower resolution than a static 1x1 pixel test pattern. Much of it is continuous in nature (subtle shade and color shifts from dark to light areas, rather than hard-edged single-pixel fields of a test pattern). Movie detail is also moving detail. Our eyes find it harder to distinguish subtleties of detail when the macro contents of the image are moving about (once again as distinguished from the static detail of a test pattern). The human eye is much better at detecting changes in a static scene with high contrast changes over small areas (a test pattern) than it is with a moving scene with low contrast shifts across similarly small areas (a typical movie).
In my opinion, the Cine4Home test was a useful, yet technical, demonstration of the viability of extrapolation algorithms when used with static detail. As an indicator (as seemed to be claimed) of significant detail loss when using an anamorphic lens passing a vertically stretched image, it was less useful. The Cine4Home test was not comparing apples with apples. It did not take into account the factors mentioned above, which can be summarized as "movies are not test patterns".
Brightness
Because the image when an anamorphic lens is employed is only being widened and not made higher (hence "Constant Image Height") the loss of brightness is less than when the picture is enlarged in both directions. Anamorphically stretched pixels are 4/3 times the area of the original pixels. Zoomed pixels are 16/9 times (4/3-squared) the area of the original pixels. 16/9 divided by 4/3 gives a theoretical 33.3% brighter picture for anamorphically stretched images.
From this some transmission loss - the amount of light lost as the projection beam passes through the optics of the lens - needs to be subtracted. For an anti-reflection coated (AR) system, figure about 0.5% per surface, giving (roughly) something like 4% for a 4-element lens. Let's rule it off at 5% for luck.
So now your anamorphic system is only 28% brighter than your zoom system.
Next we need to subtract some more brightness (or actually add brightness to the zoom system, which amounts to the same thing) due to the greater efficiency of a zoom lens when it is zoomed out for a wider picture. Normally, doubling the dimensions of a projected picture would leave the enlarged picture 1/4 as bright as the original, but due to the optics of zoom lenses used for projection, this figure is closer to 1/3 as bright. Yes, there is still some loss, but it is not as much as you'd think merely from applying a straight area comparison between the sizes of the "before" and "after" screen images. So, our nominal 28% brightness dividend from using an anamorphic lens most likely comes down to around a working total of 10%-20% brighter, depending on the optics of the projector.
Conclusions
1. Overall, effective (i.e. noticeable) resolution loss with an anamorphic lens is not as much as has been claimed. There is a clear dividend optically, if good optics are used (color-aberration corrected, AR coated, quality glass, good design).
2. Whether this optical resolution dividend is cancelled out by the digital stretch process is arguable. In my personal view, it is not entirely cancelled out, due to the nature and resolution content of the image being viewed (especially if the images are movies). My opinion is that, given good optics, anamorphic systems have the potential to be sharper than zoom systems, and more "pleasing" to look at from closer distances (i.e. in small HTs) due to the smaller pixel area.
3. An anamorphic system is most likely from 10%-20% brighter than a zoomed system. Once again, good optics are a prerequisite.
4. All of the above depends on good optics and the individual projection system, comprising projector (of course!), room size, seating arrangements and so on.
5. There are other things to be considered too which were not discussed above. Some systems (particularly DLP) do not have the zoom and offsetting capabilities that are required for the Zoom Method. Or if they do, the room is too small. Some systems do not have vertical stretch. Pincushion distortion is another bug bear. If you don't like pincushion distortion, zoom (although pincushion is pretty small at TRs over 2.0). These considerations should all be weighed when deciding whether to use a lens or zooming.
Personal Observations
For the record, I use a cylindrical lens of my own design with a JVC HD-100 (RS2 in the US). I believe my optics are very good (pats self on back). It resolves a 1x1 pixel dot pattern cleanly all over the screen. It does not affect focus whether the lens is in or out of the beam.
There is quite a noticeable drop in brightness between the anamorphic lens setup and zooming. Switching between 16:9 and zoomed 2.35:1 pictures is a real pain with the JVC HD-100. You can't just zoom, re-offset the lens and re-focus. Refocus and zoom are strictly menu operations and you have to go to a fair amount of trouble to access these functions. This re-alignment of the system can take 2 minutes setting up and another 2 minutes restoring things to normal.
By contrast, if I want to switch between 16:9 and 2.35:1 anamorphically I just slide my lens out of the way in literally 2 seconds... no re-focus, no-re-zoom, no re-offsetting. Much, much quicker and more convenient.
And a better, brighter image, too.
(Room details: screen size 120" x 51", Throw Distance ~15 feet, Throw Ratio ~2.1)
