FYI, as I
deprecate rumour and prefer hard facts, I did some tests and here are the results:
Download testsuite now:
JPGLOSSY.ZI7 (1 MiB | 7-ZIP file)
1. JPG lossless / histogram
Clearly not correct. I ran some tests before making my previous post. When I rotated an image 90 degrees & then compared the histograms, there was a very small change.
I can reproduce the problem. The so called "lossless JPG transformation" is in fact lossy, check "JPG400A.JPG" , "JPG400B.JPG" , "BMP400A.BMP" , "BMP400B.BMP" , "BMP400C.BMP" - "A" and "C" should be identical but aren't. This is an implementation BUG / flaw

and had been already discussed here:
t=19014 "Lossless JPEG rotation only lossless at 360 degrees?" As the output image has tiny bitmap differences (by +/-1 per pixel channel), the histogram also is different. Because the histogram
MUST be identical if the rotate / mirror transformation is lossless.
2. JPG cropped by 8 or 16 ???
*shrug* The warning popup from xnview states 8, that is what I based that statement on.
I can reproduce the problem, see ^^^ shot. The crop can be up to 15 pixels, pick "JPG415.JPG" and test, you'll quickly find out that it crops down to 400, not 408. The message is faulty in multiple ways, there are no "unused pixels" removed, it should say:
JPEG lossless operation will directly modify original file(s) on storage media, and if the size is not an integer multiple of 16, it may unrecoverably crop away up to 15 pixels at right and bottom of original picture.
See also :
http://newsgroup.xnview.com/viewtopic.php?t=20032 "JPEG Lossless Join"
3. GIF vs PNG / horizontal vs vertical
I said image CONTENT, not images. ie, A horizontal stripe compresses better than an identical vertical stripe.
Yeah indeed shots with text compress worse if rotated making the text vertical, see "CROPMESH.GIF" , "CROPMESV.GIF" , "CROPMESH.JPG" , "CROPMESV.JPG" , "WISTAH.JPG" , "WISTAV.JPG" , "CROPMESH.PNG" , "CROPMESV.PNG" , "PPHOT24H.PNG" , "PPHOT24V.PNG" , "WISTAH.PNG" and "WISTAV.PNG". This is primarily a problem of GIF (bloat increase by factor 1.38), less of PNG (increase factor only 1.19), and almost no problem for JPG (unsurprisingly, considering the transformations included in JPG compression). You can also see that
GIF is 4.8 x worse than PNG on "CROPMESV" bitmap, and no GIF's at all are provided for "WISTA" bitmaps (consider 13'215 colours). Apparently there are
good reasons why I deprecate GIF 
. OTOH the "WISTA" bitmaps do show that JPG can be much smaller than PNG, but looks very crappy then (quality value was 30), with quality value of 94 the JPG size egalizes PNG, and there is still noise in, although barely visible without zoom-up.