I noticed that Absolute gives more punch and brightness to the photos, and the whites are more white. When I use Relative or Perceptual there is like a grayish cast that dulls the whole picture but it's better for skin tones.
I also notice that if I use Absolute the colors are punchier but the white parts don't get any ink so they get what I think is called "gloss differential"?
What do you guys use and when? And how do you lessen the Gloss diff effect?
Which ever looks better! There's no right answer (well, unless you're doing proofing, Absolute isn't going to fly). Profile don't know anything about images, only devices. It pays to look at the soft proof and pick the intent you prefer visually. Some images will look better with one or the other, however, it's not an extreme difference.
There's no standard in how a perceptually mapping can be conducted. The ICC leaves this up tot he vendor making the profiles. So YMMV.
Absolute simulates the paper white from one device onto another hence its usually only useful for proofing. IOW, you want to see the paper white of a press simulated on an Epson printer that you're using to proof that first device. Anywhere there's a white, some ink might be laid down since the press sheet paper is different. As such, you'll forgo this expect in proofing. Also note, that other than the paper white simulation, Absolute and Relative are the same! They share the same profile tables.
Don't necessarily dismiss Saturation either. Its usually designed for 'business graphics' (pie charts) but might look OK for images. But unless you try it via a soft proof, you'll never know.