Do the math, 172.8 / 180 = 0.96 so close to 1 it's hard to understand how it would make any noticeable difference. A tiny bit less light and a tiny bit less motion blur.
Bob, I've been a bit fuzzy (pun intended) on the specifics of shutter angle when you bring it up. I just found a good discussion that includes visual examples on Red's site. Here it is for any of you in the same boat as me: http://www.red.com/learn/red-101/shutter-angle-tutorial.
Shutter angle is just another representation for shutter speed. It means that the shutter disk (in mechanical film cameras) is open 180 degrees of the full 360. When shooting 24 frames per second, 180 degrees is equivalent to 1/48 second exposure time. That is, (180/360) * 24 = (1/2) * 24 = 1/48 second. I find it much easier to just deal with time instead of angles.
I adjust my camera's shutter speed quite a bit, depending on the motion of the subject matter. At an air show, I was shooting at 1/500 or 1/1000 second because I was using my over-the-shoulder camera without a tripod and had to use software stabilization in post. Would I have shot at a slower speed, there would be excessive blurring from the rapid maneuvers of the fighter jets and the results of the stabilization would look strange. For the majority of the time, I shoot at 1/60th second exposure (for 30fps frame rate) to intentionally get blurred/softer images.
Film cameras typically record 24.000 frames per second and expose for half that time, which is 1/48 seconds. The closest matching shutter setting on many digital cameras is 1/50 seconds, which corresponds to a shutter angle of 172.8 degrees for 24.000 fps and roughly 172.6 degrees for 23.976 fps. Shooting at these angles is not so much a creative decision in favour of 4% less light and motion blur as simply a consequence of the available frame rate and shutter settings.
Since moving to DSLR, and now the GH3, I have come to have quite a different perspective on shutter-speed than I once had. I used to think of shutter-speed as ideally being twice the frame rate and not something that you would vary at all. This gives you a pretty natural motion blur, and since it worked well, why mess with success?
Then I started shooting with DSLRs that would routinely use much faster shutter speeds in order to not overexpose a large sensor with the wide aperture that I was forcing upon it for shallow depth of field. Surprisingly (to me at least), it wasn't all bad.
As was mentioned, fast shutter speeds stabilize really well. Way better than slow, nice motion blur shutter speeds. Sometimes this can be really useful.
Fast shutter speeds look juddery on fast pans or zooms, but fast pans and zooms look terrible on Youtube anyway because of the data compression. I find that by limiting the camera motion, I can get away with fast shutter speeds.
I can still do fast camera moves by simply keyframing in a little blur on the axis of the movement during the move. I don't even worry about it anymore.
Your eye gets used to faster shutter speeds and learns to ignore them. In fact, I see fast shutter speeds everywhere these days. They are all over the place on Youtube and Vimeo. Used to drive me nuts. Now I hardly notice. I think the same thing is happening to the audience as a whole because I never see this mentioned, even in video specific forums anymore. That is, I see people post things with lots of judder, and neither I nor anyone else even complains anymore. I think our eyes have just learned to live with and ignore it because I'm not just being nice, it really doesn't bother me anymore.
The thing with judder is it depends on so many things other than shutter angle.
Today I was have a bit of down time playing around with our FS700. Switched it into 25p with a 180 deg shutter. The HDMI output was connected to a HTDV. Just walking past the camera I looked a juddery mess and everyone is saying "see Bob, never shoot progressive", sigh, I shoot mostly 25p for YT and it looks just fine and playing back a mp4 from a thumb drive in the same TV it looks fine as well.
So, digging into the FS700's menu I found I can send the 25p out the HDMI socket as 25PsF50. Now the HDTV no longer shows such a juddery mess, still not as good as the mp4 encoded out of Vegas though. Why this is happening I haven't a clue.