The main advantage of underexposing is that you reduce the chance of blown highlights, assuming that you care.
The disadvantage is that you cannot review the image on the spot (the same is true for ETTR) so you might be disappointed when you start to convert the raw file.
There is no technical advantage to underexposing. None.
Most people don't seem to understand precisely what "ISO invariance" is, and there are all sorts of claims about which cameras are or are not. Here is what Thom Hogan said:
The key words are "constant slope". That means the curve will be essentially a straight line for any portion which can be called "ISO invariant".
Below is an image showing charts for two cameras, one of which is perhaps the least "invariant" DSLR that I know of, and one of which is fairly near to a straight line. (I've trimmed the screen shot to avoid identifying the exact models. Note that the graph is from Bill Claff's webpage.)
On the webpage it is easy to get exact numbers for the sample points. Here is a chart showing values over a range from ISO 400 to ISO 800 for each camera,
ISO Top Graph Bottom Graph
400 9.63 8.03
503 9.33 7.68
636 8.97 6.43
800 8.64 7.30
For the top graph each higher step in ISO causes a linear change in the Dynamic Range. With the bottom graph, for the non ISO variant camera, the ISO change is not linear and the worst case is a 1/3 step higher from ISO 503 to ISO 636 actually reduces the Dynamic Range lower than it will be at ISO 800. Note that on even multiples such as 100, 200, 400, 800 and so on the change is perhaps not exactly 1 stop less Dynamic Range but fairly close to it (if we plotted only those values it would be a constant slope).
Okay, that is what defines ISO Invariance. Now the question is what significance is there? The answer is virtually none, and certainly not the claims that it means one can shoot at base ISO and get exactly the same image as if it were shot at a higher ISO!
Most of the comments to the effect that there is some advantage all center on shooting at something less than ISO 800. Note that the Dynamic Range, even with the lesser of these two cameras, is 7.3 fstops at that ISO. Most JPEG images have less than 7 fstops of Dynamic Range and most prints less than 5. That means unless significant gamma curve manipulation is done there will not be any visible noise in the shadows (the black point will be higher than the read noise).
The supposed equivalence is an artifact of the image not being displayed with enough Dynamic Range to see the noise and has no relevance to "ISO Invariance". The effect would be essentially identical with both of these cameras!
The advantages of using analog gain before the ADC would be seen for both cameras. The disadvantages of digital multiplication in correcting an underexposed image would also be identical for both cameras.
The entire concept that ISO non-variance is of some value is pseudo science based on attributing sometimes valid (or not) observations to the wrong cause.